diff --git a/DESCRIPTION b/DESCRIPTION index 12959c7..a36bb8e 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,7 +1,7 @@ Package: VineCopula Type: Package Title: Statistical Inference of Vine Copulas -Version: 2.5.2 +Version: 2.6.0 Description: Provides tools for the statistical analysis of regular vine copula models, see Aas et al. (2009) and Dissman et al. (2013) . diff --git a/NEWS.md b/NEWS.md index 92c9ac6..95bb331 100644 --- a/NEWS.md +++ b/NEWS.md @@ -1,10 +1,15 @@ -VineCopula 2.5.0 +VineCopula 2.6.0 ---------------------------------------------------------------- NEW FEATURES * add `RVineCDF()` function for cumulative distribution of vine copulas models (#97). +BUG FIX + +* Fix read past parameter boundary in `difflPDF_mod` (non-critical). + + VineCopula 2.5.1 ---------------------------------------------------------------- diff --git a/docs/404.html b/docs/404.html index 5343c41..431cccb 100644 --- a/docs/404.html +++ b/docs/404.html @@ -18,7 +18,7 @@ - +
@@ -49,7 +49,7 @@
  • - +
    • @@ -60,7 +60,7 @@
    - +
    @@ -88,16 +88,16 @@

    Page not found (404)

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/authors.html b/docs/authors.html index 04c0ea3..c889650 100644 --- a/docs/authors.html +++ b/docs/authors.html @@ -3,7 +3,7 @@ - +
    @@ -31,14 +31,14 @@
    - +
    @@ -47,57 +47,57 @@

    Authors and Citation

    - +
    • -

      Thomas Nagler. Author, maintainer. +

      Thomas Nagler. Author, maintainer.

    • -

      Ulf Schepsmeier. Author. +

      Ulf Schepsmeier. Author.

    • -

      Jakob Stoeber. Author. +

      Jakob Stoeber. Author.

    • -

      Eike Christian Brechmann. Author. +

      Eike Christian Brechmann. Author.

    • -

      Benedikt Graeler. Author. +

      Benedikt Graeler. Author.

    • -

      Tobias Erhardt. Author. +

      Tobias Erhardt. Author.

    • -

      Carlos Almeida. Contributor. +

      Carlos Almeida. Contributor.

    • -

      Aleksey Min. Contributor, thesis advisor. +

      Aleksey Min. Contributor, thesis advisor.

    • -

      Claudia Czado. Contributor, thesis advisor. +

      Claudia Czado. Contributor, thesis advisor.

    • -

      Mathias Hofmann. Contributor. +

      Mathias Hofmann. Contributor.

    • -

      Matthias Killiches. Contributor. +

      Matthias Killiches. Contributor.

    • -

      Harry Joe. Contributor. +

      Harry Joe. Contributor.

    • -

      Thibault Vatter. Contributor. +

      Thibault Vatter. Contributor.

    @@ -111,13 +111,13 @@

    Citation

    Nagler T, Schepsmeier U, Stoeber J, Brechmann E, Graeler B, Erhardt T (2024). VineCopula: Statistical Inference of Vine Copulas. -R package version 2.5.1, https://github.com/tnagler/VineCopula. +R package version 2.6.0, https://github.com/tnagler/VineCopula. 

    @Manual{,
   title = {VineCopula: Statistical Inference of Vine Copulas},
   author = {Thomas Nagler and Ulf Schepsmeier and Jakob Stoeber and Eike Christian Brechmann and Benedikt Graeler and Tobias Erhardt},
   year = {2024},
-  note = {R package version 2.5.1},
+  note = {R package version 2.6.0},
   url = {https://github.com/tnagler/VineCopula},
 }
    @@ -132,15 +132,15 @@

    Citation

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/index.html b/docs/index.html index b12e69f..809576a 100644 --- a/docs/index.html +++ b/docs/index.html @@ -19,7 +19,7 @@ - +
    @@ -50,7 +50,7 @@
  • - +
    • @@ -61,7 +61,7 @@
    - +
    @@ -165,7 +165,7 @@

    Vine copula modeling: the RVine-f

  • RVineGoFTest: Goodness-of-Fit tests for a vine copula model (c.f., Schepsmeier, 2013, 2015). Related functions are RVineGrad, RVineHessian, RVineStdError, and RVinePIT.

  • RVineVoungTest, RVineClarkeTest: Vuong and Clarke tests for comparing two vine copula models.

  • RVinePar2Tau, RVinePar2Beta: Calculate dependence measures corresponding to a vine copula model.

    • -

  • RVinePDF, RVineLogLik, RVineAIC, RVineBIC: Calculate the density, log-likelihood, AIC, and BIC of a vine copula.

    • +

  • RVinePDF, RVineCDF, RVineLogLik, RVineAIC, RVineBIC: Calculate the density, cumulative distribution, log-likelihood, AIC, and BIC of a vine copula.

    • @@ -453,16 +453,16 @@

    Developers

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/news/index.html b/docs/news/index.html index a174ab3..1be0b96 100644 --- a/docs/news/index.html +++ b/docs/news/index.html @@ -3,7 +3,7 @@ - +
    @@ -31,14 +31,14 @@
    - +
    @@ -48,7 +48,14 @@

    Changelog

    -

    VineCopula 2.5.1

    +

    VineCopula 2.6.0

    +

    NEW FEATURES

    +
    • add RVineCDF() function for cumulative distribution of vine copulas models (#97).
      • +

    BUG FIX

    +
    • Fix read past parameter boundary in difflPDF_mod (non-critical).
      • +
    +
    +

    VineCopula 2.5.12024-08-19

    BUG FIXES

    • fix log-derivatives of 90 and 270 degree rotations.

    • Fix missing BB8 in BiCopName().

      • @@ -314,8 +321,8 @@

      VineCopula 1.5

    • BiCopEst: extend search interval for Tawn MLE to avoid optim-errors.

    • BiCopEst: fix for optim error (‘non-finite value supplied’).

    • RVineSim: reorder U so that it corresponds to the order of RVM.

      • -

    • RVineCor2pcor: include normalization step for a more intuitive behavior, bug fix for d = 2, 3 and d > 9.

      • -

    • RVinePcor2cor: bug fixes for d = 2 and d > 9.

      • +

    • RVineCor2pcor: include normalization step for a more intuitive behavior, bug fix for d=2,3d = 2, 3 and d>9d > 9.

      • +

    • RVinePcor2cor: bug fixes for d=2d = 2 and d>9d > 9.

    • RVineCopSelect: RVM object now uses variable names as provided by data.

    @@ -367,7 +374,7 @@

    VineCopula 1.

    VineCopula 1.2-1

    NEW FEATURES

    -

    • RVineSim allows to commit a (N x d)-matrix of U[0,1] random variates to be transformed to the copula sample. For example if you want to use quasi random variables instead of the pseudo random variables implemented in R. (Thanks to Marius Hofert)

      • +

      • RVineSim allows to commit a (N x d)-matrix of U[0,1]U[0,1] random variates to be transformed to the copula sample. For example if you want to use quasi random variables instead of the pseudo random variables implemented in R. (Thanks to Marius Hofert)

      • The package now contains class wrappers that are compatible with the copula class from the copula R-package. These include all bivariate families currently implemented: The class representation for different rotated families of e.g the BB6 family are represented as BB6Copula, r90B6Copula, surBB6Copula and r270BB6Copula. These bivariate classes are fully compatible with the standard copula methods such as dCopula, pCopula, rCopula or fitCopula including persp and contour. A vine copula can as well be coerced into a class representation of vineCopula. However, the support of the standard methods is limited. See the corresponding help pages for details. Earlier introduced R-wrapper of C-functions have been removed, as they are no longer needed by the spcopula R-package.

      • Added parameter verbose to RVineLogLik to allow to suppress some debug output.

      BUG FIXES

      @@ -446,15 +453,15 @@

      VineCopula 1.1
      -

      Site built with pkgdown 2.0.9.

      +

      Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml index b0f92a2..0ca7f6b 100644 --- a/docs/pkgdown.yml +++ b/docs/pkgdown.yml @@ -1,6 +1,5 @@ -pandoc: 3.1.11 -pkgdown: 2.0.9 +pandoc: '3.2' +pkgdown: 2.1.1 pkgdown_sha: ~ articles: {} -last_built: 2024-08-19T13:24Z - +last_built: 2024-12-16T19:42Z diff --git a/docs/reference/BetaMatrix.html b/docs/reference/BetaMatrix.html index b4b85b7..03462b4 100644 --- a/docs/reference/BetaMatrix.html +++ b/docs/reference/BetaMatrix.html @@ -3,7 +3,7 @@ - +
    @@ -31,14 +31,14 @@

    - +
    @@ -58,15 +58,15 @@

    Matrix of Empirical Blomqvist's Beta Values

    Arguments

    -
    data
    + + +
    data

    An N x d data matrix.

    Value

    - - -

    Matrix of the empirical Blomqvist's betas.

    +

    Matrix of the empirical Blomqvist's betas.

    References

    @@ -155,15 +155,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCop.html b/docs/reference/BiCop.html index 9062a7f..5999819 100644 --- a/docs/reference/BiCop.html +++ b/docs/reference/BiCop.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,8 +60,10 @@

    Constructing BiCop-objects

    Arguments

    -
    family
    -

    An integer defining the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 = rotated Clayton copula (90 degrees)
    + + +

    family
    +

    An integer defining the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    @@ -85,24 +87,24 @@

    Arguments

    `234` = rotated Tawn type 2 copula (270 degrees)

    -
    par
    +
    par

    Copula parameter.

    -
    par2
    +
    par2

    Second parameter for bivariate copulas with two parameters (t, BB1, BB6, BB7, BB8, Tawn type 1 and type 2; default is par2 = 0). par2 should be an positive integer for the Students's t copula family = 2.

    -
    tau
    +
    tau

    numeric; value of Kendall's tau; has to lie in the interval (-1, 1). Can only be used with one-parameter families and the t copula. If tau is provided, par will be ignored.

    -
    check.pars
    +
    check.pars

    logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

    @@ -110,9 +112,7 @@

    Arguments

    Value

    - - -

    An object of class BiCop(). It is a list containing +

    An object of class BiCop(). It is a list containing information about the bivariate copula. Its components are:

    family, par, par2

    copula family number and parameter(s),

    @@ -240,15 +240,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopCDF.html b/docs/reference/BiCopCDF.html index a8d9905..963bb39 100644 --- a/docs/reference/BiCopCDF.html +++ b/docs/reference/BiCopCDF.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,13 +60,15 @@

    Distribution Function of a Bivariate Copula

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    numeric vectors of equal length with values in \([0,1]\).

    -
    family
    +
    family

    integer; single number or vector of size length(u1); -defines the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 = rotated Clayton copula (90 degrees)
    +defines the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    @@ -90,23 +92,23 @@

    Arguments

    `234` = rotated Tawn type 2 copula (270 degrees)

    -
    par
    +
    par

    numeric; single number or vector of size length(u1); copula parameter.

    -
    par2
    +
    par2

    numeric; single number or vector of size length(u1); second parameter for bivariate copulas with two parameters (BB1, BB6, BB7, BB8, Tawn type 1 and type 2; default: par2 = 0).

    -
    obj
    +
    obj

    BiCop object containing the family and parameter specification.

    -
    check.pars
    +
    check.pars

    logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

    @@ -114,9 +116,7 @@

    Arguments

    Value

    - - -

    A numeric vector of the bivariate copula distribution function

    • of the copula family

      • +

      A numeric vector of the bivariate copula distribution function

      • of the copula family

      • with parameter(s) par, par2

      • evaluated at u1 and u2.

    @@ -297,15 +297,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopCheck.html b/docs/reference/BiCopCheck.html index 187f348..bbea3d0 100644 --- a/docs/reference/BiCopCheck.html +++ b/docs/reference/BiCopCheck.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,8 +60,10 @@

    Check for family/parameter consistency in bivariate copula models

    Arguments

    -
    family
    -

    An integer defining the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 = rotated Clayton copula (90 degrees)
    + + +

    family
    +

    An integer defining the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    @@ -85,24 +87,22 @@

    Arguments

    `234` = rotated Tawn type 2 copula (270 degrees)

    -
    par
    +
    par

    Copula parameter.

    -
    par2
    +
    par2

    Second parameter for bivariate copulas with two parameters (t, BB1, BB6, BB7, BB8, Tawn type 1 and type 2; default is par2 = 0).

    -
    ...
    +
    ...

    used internally.

    Value

    - - -

    A logical indicating whether the family can be used with the parameter +

    A logical indicating whether the family can be used with the parameter specification.

    @@ -116,7 +116,7 @@

    Examples

    BiCopCheck(3, 1) # works #> [1] TRUE -if (FALSE) BiCopCheck(3, -1) # does not work (only positive parameter is allowed) +if (FALSE) BiCopCheck(3, -1) # does not work (only positive parameter is allowed) # \dontrun{}
    @@ -132,15 +132,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopChiPlot.html b/docs/reference/BiCopChiPlot.html index 2b478d9..fe27825 100644 --- a/docs/reference/BiCopChiPlot.html +++ b/docs/reference/BiCopChiPlot.html @@ -3,7 +3,7 @@ - +
    @@ -31,14 +31,14 @@
    - +
    @@ -58,28 +58,32 @@

    Chi-plot for Bivariate Copula Data

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    Data vectors of equal length with values in \([0,1]\).

    -
    PLOT
    +
    PLOT

    Logical; whether the results are plotted. If PLOT = FALSE, the values lambda, chi and control.bounds are returned (see below; default: PLOT = TRUE).

    -
    mode
    +
    mode

    Character; whether a general, lower or upper chi-plot is calculated. Possible values are mode = "NULL", "upper" and "lower".
    "NULL" = general chi-plot (default)
    "upper" = upper chi-plot
    "lower" = lower chi-plot

    -
    ...
    +
    ...

    Additional plot arguments.

    Value

    -
    lambda
    + + +
    lambda

    Lambda-statistics (x-axis).

    chi

    Chi-statistics @@ -116,7 +120,7 @@

    Details

    independence it holds that \(\chi_i \sim \mathcal{N}(0,\frac{1}{N})\) and \(\lambda_i \sim \mathcal{U}[-1,1]\) asymptotically, i.e., values of -\(\chi_i\) close to zero indicate independence---corresponding to +\(\chi_i\) close to zero indicate independence—corresponding to \(F_{1, 2}=F_{1}F_{2}\).

    When plotting these quantities, the pairs of \(\left(\lambda_i, \chi_i \right)\) will tend to be located above zero for @@ -186,15 +190,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopCompare.html b/docs/reference/BiCopCompare.html index 8c635bd..d689952 100644 --- a/docs/reference/BiCopCompare.html +++ b/docs/reference/BiCopCompare.html @@ -6,7 +6,7 @@ - +
    @@ -34,14 +34,14 @@
    - +
    @@ -64,18 +64,20 @@

    Shiny app for bivariate copula selection

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    Data vectors of equal length with values in \([0,1]\).

    -
    familyset
    +
    familyset

    Vector of bivariate copula families to select from. The vector has to include at least one bivariate copula family that allows for positive and one that allows for negative dependence. If familyset = NA (default), selection among all possible families is performed. If a vector of negative numbers is provided, selection among all but abs(familyset) families is performed. Coding of bivariate copula -families:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 = rotated Clayton copula (90 degrees)
    +families:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    @@ -99,16 +101,14 @@

    Arguments

    `234` = rotated Tawn type 2 copula (270 degrees)

    -
    rotations
    +
    rotations

    If TRUE, all rotations of the families in familyset are included (or subtracted).

    Value

    - - -

    A BiCop() object containing the model selected by the +

    A BiCop() object containing the model selected by the user.

    @@ -122,7 +122,7 @@

    Examples

    data(daxreturns) # find a suitable copula family for the first two stocks -if (FALSE) fit <- BiCopCompare(daxreturns[, 1], daxreturns[, 2]) +if (FALSE) fit <- BiCopCompare(daxreturns[, 1], daxreturns[, 2]) # \dontrun{}
    @@ -138,15 +138,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopCondSim.html b/docs/reference/BiCopCondSim.html index 7a982d9..616d673 100644 --- a/docs/reference/BiCopCondSim.html +++ b/docs/reference/BiCopCondSim.html @@ -6,7 +6,7 @@ - +
    @@ -34,14 +34,14 @@
    - +
    @@ -73,22 +73,24 @@

    Conditional simulation from a Bivariate Copula

    Arguments

    -
    N
    + + +
    N

    Number of observations simulated.

    -
    cond.val
    +
    cond.val

    numeric vector of length N containing the values to condition on.

    -
    cond.var
    +
    cond.var

    either 1 or 2; the variable to condition on.

    -
    family
    +
    family

    integer; single number or vector of size N; defines the -bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 = rotated Clayton copula (90 degrees)
    +bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    @@ -112,24 +114,24 @@

    Arguments

    `234` = rotated Tawn type 2 copula (270 degrees)

    -
    par
    +
    par

    numeric; single number or vector of size N; copula parameter.

    -
    par2
    +
    par2

    numeric; single number or vector of size N; second parameter for bivariate copulas with two parameters (t, BB1, BB6, BB7, BB8, Tawn type 1 and type 2; default: par2 = 0). par2 should be a positive integer for the Students's t copula family = 2.

    -
    obj
    +
    obj

    BiCop object containing the family and parameter specification.

    -
    check.pars
    +
    check.pars

    logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

    @@ -137,9 +139,7 @@

    Arguments

    Value

    - - -

    A length N vector of simulated from conditional distributions +

    A length N vector of simulated from conditional distributions related to bivariate copula with family and parameter(s) par, par2.

    @@ -194,15 +194,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopDeriv.html b/docs/reference/BiCopDeriv.html index e9274ba..e5e9b63 100644 --- a/docs/reference/BiCopDeriv.html +++ b/docs/reference/BiCopDeriv.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -70,13 +70,15 @@

    Derivatives of a Bivariate Copula Density

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    numeric vectors of equal length with values in \([0,1]\).

    -
    family
    +
    family

    integer; single number or vector of size length(u1); -defines the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; ``survival Joe'')
    23 = rotated Clayton copula (90 degrees)
    +defines the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; “survival Joe”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `33` = rotated Clayton copula (270 degrees)
    @@ -84,34 +86,34 @@

    Arguments

    `36` = rotated Joe copula (270 degrees)

    -
    par
    +
    par

    numeric; single number or vector of size length(u1); copula parameter.

    -
    par2
    +
    par2

    integer; single number or vector of size length(u1); second parameter for the t-Copula; default is par2 = 0, should be an positive integer for the Students's t copula family = 2.

    -
    deriv
    +
    deriv

    Derivative argument
    "par" = derivative with respect to the first parameter (default)
    "par2" = derivative with respect to the second parameter (only available for the t-copula)
    "u1" = derivative with respect to the first argument u1
    "u2" = derivative with respect to the second argument u2

    -
    log
    +
    log

    Logical; if TRUE than the derivative of the log-likelihood is returned (default: log = FALSE; only available for the derivatives with respect to the parameter(s) (deriv = "par" or deriv = "par2")).

    -
    obj
    +
    obj

    BiCop object containing the family and parameter specification.

    -
    check.pars
    +
    check.pars

    logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

    @@ -119,9 +121,7 @@

    Arguments

    Value

    - - -

    A numeric vector of the bivariate copula derivative

    • of the copula family

      • +

      A numeric vector of the bivariate copula derivative

      • of the copula family

      • with parameter(s) par, par2

      • with respect to deriv,

      • evaluated at u1 and u2.

        • @@ -216,15 +216,15 @@

        Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopDeriv2.html b/docs/reference/BiCopDeriv2.html index a50573e..93ccdf8 100644 --- a/docs/reference/BiCopDeriv2.html +++ b/docs/reference/BiCopDeriv2.html @@ -5,7 +5,7 @@ - +
    @@ -33,14 +33,14 @@
    - +
    @@ -71,13 +71,15 @@

    Second Derivatives of a Bivariate Copula Density

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    numeric vectors of equal length with values in \([0,1]\).

    -
    family
    +
    family

    integer; single number or vector of size length(u1); -defines the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; ``survival Joe'')
    23 = rotated Clayton copula (90 degrees)
    +defines the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; “survival Joe”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `33` = rotated Clayton copula (270 degrees)
    @@ -85,17 +87,17 @@

    Arguments

    `36` = rotated Joe copula (270 degrees)

    -
    par
    +
    par

    Copula parameter.

    -
    par2
    +
    par2

    integer; single number or vector of size length(u1); second parameter for the t-Copula; default is par2 = 0, should be an positive integer for the Students's t copula family = 2.

    -
    deriv
    +
    deriv

    Derivative argument
    "par" = second derivative with respect to the first parameter (default)
    "par2" = second derivative with respect to the second parameter (only available for the t-copula)
    "u1" = second derivative with respect to @@ -110,12 +112,12 @@

    Arguments

    (only available for the t-copula)

    -
    obj
    +
    obj

    BiCop object containing the family and parameter specification.

    -
    check.pars
    +
    check.pars

    logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

    @@ -123,9 +125,7 @@

    Arguments

    Value

    - - -

    A numeric vector of the second-order bivariate copula derivative

    • of the copula family

      • +

      A numeric vector of the second-order bivariate copula derivative

      • of the copula family

      • with parameter(s) par, par2

      • with respect to deriv

      • evaluated at u1 and u2.

        • @@ -222,15 +222,15 @@

        Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopEst.html b/docs/reference/BiCopEst.html index 838f343..1d86111 100644 --- a/docs/reference/BiCopEst.html +++ b/docs/reference/BiCopEst.html @@ -5,7 +5,7 @@ - +
    @@ -33,14 +33,14 @@
    - +
    @@ -71,12 +71,14 @@

    Parameter Estimation for Bivariate Copula Data

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    Data vectors of equal length with values in \([0,1]\).

    -
    family
    -

    An integer defining the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 = rotated Clayton copula (90 degrees)
    +

    family
    +

    An integer defining the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    @@ -100,7 +102,7 @@

    Arguments

    `234` = rotated Tawn type 2 copula (270 degrees)

    -
    method
    +
    method

    indicates the estimation method: either maximum likelihood estimation (method = "mle"; default) or inversion of Kendall's tau (method = "itau"). For method = "itau" only @@ -109,31 +111,29 @@

    Arguments

    interval (2, 10].

    -
    se
    +
    se

    Logical; whether standard error(s) of parameter estimates is/are estimated (default: se = FALSE).

    -
    max.df
    +
    max.df

    Numeric; upper bound for the estimation of the degrees of freedom parameter of the t-copula (default: max.df = 30).

    -
    max.BB
    +
    max.BB

    List; upper bounds for the estimation of the two parameters (in absolute values) of the BB1, BB6, BB7 and BB8 copulas
    (default: max.BB = list(BB1=c(5,6),BB6=c(6,6),BB7=c(5,6),BB8=c(6,1))).

    -
    weights
    +
    weights

    Numerical; weights for each observation (optional).

    Value

    - - -

    An object of class BiCop(), augmented with the following +

    An object of class BiCop(), augmented with the following entries:

    se, se2

    standard errors for the parameter estimates (if @@ -334,15 +334,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopEstList.html b/docs/reference/BiCopEstList.html index d99165c..c76e5ef 100644 --- a/docs/reference/BiCopEstList.html +++ b/docs/reference/BiCopEstList.html @@ -5,7 +5,7 @@ - +
    @@ -33,14 +33,14 @@
    - +
    @@ -62,16 +62,18 @@

    List of Maximum Likelihood Estimates for Several Bivariate Copula Families

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    Data vectors of equal length with values in \([0,1]\).

    -
    familyset
    +
    familyset

    Vector of bivariate copula families to select from. The vector has to include at least one bivariate copula family that allows for positive and one that allows for negative dependence. If familyset = NA (default), selection among all possible families is -performed. Coding of bivariate copula families:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 = rotated Clayton copula (90 degrees)
    +performed. Coding of bivariate copula families:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    @@ -95,27 +97,25 @@

    Arguments

    `234` = rotated Tawn type 2 copula (270 degrees)

    -
    weights
    +
    weights

    Numerical; weights for each observation (optional).

    -
    rotations
    +
    rotations

    If TRUE, all rotations of the families in familyset are included.

    -
    ...
    +
    ...

    further arguments passed to BiCopEst().

    Value

    - - -

    A list containing

    +

    A list containing

    models

    a list of BiCop() objects corresponding to the -`familyset`` (only families corresponding to the sign of the empirical +`familyset“ (only families corresponding to the sign of the empirical Kendall's tau are used),

    summary
    @@ -178,15 +178,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopGofTest.html b/docs/reference/BiCopGofTest.html index 9046aa4..c1875fa 100644 --- a/docs/reference/BiCopGofTest.html +++ b/docs/reference/BiCopGofTest.html @@ -7,7 +7,7 @@ - +
    @@ -35,14 +35,14 @@
    - +
    @@ -76,14 +76,16 @@

    Goodness-of-Fit Test for Bivariate Copulas

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    Numeric vectors of equal length with values in \([0,1]\).

    -
    family
    -

    An integer defining the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula) (only for method = "white"; see details)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula (only for method = "kendall")
    8 = BB6 copula (only for method = "kendall")
    9 = BB7 copula (only for method = "kendall")
    10 = BB8 copula (only for method ="kendall")
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1''; -only for method = "kendall")
    18 = rotated BB6 copula (180 degrees; survival BB6''; only for `method = "kendall"`)\cr `19` = rotated BB7 copula (180 degrees; survival BB7''; -only for method = "kendall")
    20 = rotated BB8 copula (180 degrees; ``survival BB8''; +

    family
    +

    An integer defining the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula) (only for method = "white"; see details)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula (only for method = "kendall")
    8 = BB6 copula (only for method = "kendall")
    9 = BB7 copula (only for method = "kendall")
    10 = BB8 copula (only for method ="kendall")
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”; +only for method = "kendall")
    18 = rotated BB6 copula (180 degrees; survival BB6''; only for `method = "kendall"`)\cr `19` = rotated BB7 copula (180 degrees; survival BB7”; +only for method = "kendall")
    20 = rotated BB8 copula (180 degrees; “survival BB8”; only for method = "kendall")
    `23` = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    @@ -101,50 +103,46 @@

    Arguments

    `40` = rotated BB8 copula (270 degrees; only for `method = "kendall"`)

    -
    par
    +
    par

    Copula parameter (optional).

    -
    par2
    +
    par2

    Second parameter for bivariate t-copula (optional); default: par2 = 0.

    -
    method
    +
    method

    A string indicating the goodness-of-fit method:
    "white" = goodness-of-fit test based on White's information matrix equality (default)
    "kendall" = goodness-of-fit test based on Kendall's process

    -
    max.df
    +
    max.df

    Numeric; upper bound for the estimation of the degrees of freedom parameter of the t-copula (default: max.df = 30).

    -
    B
    +
    B

    Integer; number of bootstrap samples (default: B = 100). For B = 0 only the the test statistics are returned.
    WARNING: If B is chosen too large, computations will take very long.

    -
    obj
    +
    obj

    BiCop object containing the family and parameter specification.

    Value

    - - -

    For method = "white":

    +

    For method = "white":

    p.value

    Asymptotic p-value.

    statistic

    The observed test statistic.

    -


    - - -

    For method ="kendall"

    +


    +For method ="kendall"

    p.value.CvM

    Bootstrapped p-value of the goodness-of-fit test using the Cramer-von Mises statistic (if B > 0).

    @@ -217,7 +215,6 @@

    Author

    Examples

    
 # simulate from a bivariate Clayton copula
-set.seed(123)
 simdata <- BiCopSim(100, 3, 2)
 u1 <- simdata[,1]
 u2 <- simdata[,2]
@@ -286,15 +283,15 @@ 
    Examples
    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopHfunc.html b/docs/reference/BiCopHfunc.html index 349880a..bed4d4a 100644 --- a/docs/reference/BiCopHfunc.html +++ b/docs/reference/BiCopHfunc.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -64,13 +64,15 @@

    Conditional Distribution Function of a Bivariate Copula

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    numeric vectors of equal length with values in \([0,1]\).

    -
    family
    +
    family

    integer; single number or vector of size length(u1); -defines the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 = rotated Clayton copula (90 degrees)
    +defines the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    @@ -94,24 +96,24 @@

    Arguments

    `234` = rotated Tawn type 2 copula (270 degrees)

    -
    par
    +
    par

    numeric; single number or vector of size length(u1); copula parameter.

    -
    par2
    +
    par2

    numeric; single number or vector of size length(u1); second parameter for bivariate copulas with two parameters (t, BB1, BB6, BB7, BB8, Tawn type 1 and type 2; default: par2 = 0). par2 should be an positive integer for the Students's t copula family = 2.

    -
    obj
    +
    obj

    BiCop object containing the family and parameter specification.

    -
    check.pars
    +
    check.pars

    logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

    @@ -119,9 +121,7 @@

    Arguments

    Value

    - - -

    BiCopHfunc returns a list with

    +

    BiCopHfunc returns a list with

    hfunc1

    Numeric vector of the conditional distribution function (h-function) of the copula family with parameter(s) @@ -176,475 +176,6 @@

    Examples

    # h-functions of the Gaussian copula cop <- BiCop(family = 1, par = 0.5) h <- BiCopHfunc(daxreturns[, 2], daxreturns[, 1], cop) -h -#> $hfunc1 -#> [1] 6.220108e-01 3.218472e-01 7.129364e-01 4.437906e-01 5.492441e-01 -#> [6] 2.659561e-01 3.172890e-01 5.424892e-01 4.214900e-01 5.596056e-01 -#> [11] 1.808212e-01 2.110578e-02 3.268378e-01 4.186970e-01 4.539761e-01 -#> [16] 8.819727e-01 7.710018e-02 2.066970e-01 4.570489e-01 7.192216e-01 -#> [21] 3.625526e-01 7.493323e-01 4.091462e-01 3.606287e-01 9.520267e-01 -#> [26] 3.580507e-01 1.260451e-01 3.992607e-01 8.158813e-01 5.235301e-01 -#> [31] 3.404628e-01 9.973454e-02 3.719666e-01 1.666953e-02 8.525902e-01 -#> [36] 5.271848e-01 3.355021e-01 9.095176e-01 8.125316e-01 5.717504e-01 -#> [41] 6.645106e-01 6.481941e-01 3.107388e-01 7.543199e-01 3.066058e-01 -#> [46] 8.879242e-01 1.261062e-01 5.370029e-01 9.911515e-01 8.153369e-01 -#> [51] 7.832804e-01 1.739493e-01 1.891788e-01 7.224191e-01 5.028833e-01 -#> [56] 4.522016e-01 2.189110e-01 9.199584e-01 7.869646e-01 4.762817e-01 -#> [61] 8.638222e-02 4.252703e-01 1.049839e-01 3.728218e-01 2.958434e-01 -#> [66] 6.637995e-01 3.207335e-01 4.260785e-01 1.753042e-01 9.926601e-01 -#> [71] 7.040399e-01 5.598386e-02 7.551352e-02 2.291185e-01 1.864402e-01 -#> [76] 8.521182e-01 6.415018e-01 6.317190e-01 3.704021e-01 7.012655e-01 -#> [81] 2.146725e-01 9.657149e-01 6.505207e-01 6.852600e-01 6.963995e-01 -#> [86] 2.094733e-01 5.398654e-01 3.378816e-01 2.054165e-02 1.517736e-01 -#> [91] 7.462270e-01 6.324766e-01 6.053802e-01 5.225672e-01 6.995091e-01 -#> [96] 7.088544e-01 1.418718e-01 3.575292e-01 2.761821e-01 5.208735e-01 -#> [101] 8.470385e-01 3.948429e-01 7.485560e-01 8.005309e-01 4.848418e-01 -#> [106] 2.013726e-01 2.712788e-01 8.256906e-02 8.525972e-01 5.032331e-01 -#> [111] 6.371786e-01 4.639744e-01 4.729835e-01 3.866720e-01 3.431906e-01 -#> [116] 6.087868e-01 6.601683e-01 1.874756e-01 8.335392e-01 8.003653e-01 -#> [121] 3.665657e-01 1.947257e-01 5.881205e-02 4.375514e-01 9.411151e-01 -#> [126] 1.332270e-01 4.419045e-01 5.477902e-01 6.204754e-01 9.974483e-01 -#> [131] 8.600678e-02 9.031677e-01 6.408202e-01 2.446886e-01 5.065390e-01 -#> [136] 2.607399e-01 6.340757e-01 5.256622e-01 5.211369e-01 7.913579e-01 -#> [141] 4.546972e-01 7.202678e-01 7.304427e-01 6.881829e-01 8.335851e-01 -#> [146] 7.158278e-01 1.998259e-01 8.179546e-01 5.276375e-01 1.513553e-01 -#> [151] 3.252458e-01 4.025327e-01 5.493411e-01 9.425643e-01 9.942326e-01 -#> [156] 3.825682e-01 4.242957e-01 6.343864e-01 9.263601e-01 9.176409e-02 -#> [161] 3.030937e-01 6.559799e-01 6.485043e-01 1.223301e-01 5.428482e-01 -#> [166] 9.212406e-02 1.610594e-01 3.656983e-01 5.104640e-01 8.445684e-01 -#> [171] 7.804541e-02 1.599773e-01 8.064477e-01 7.440593e-01 6.936814e-01 -#> [176] 7.822910e-01 3.743332e-01 4.744443e-04 4.002331e-01 7.381080e-01 -#> [181] 7.904385e-01 5.868182e-01 2.399785e-01 5.398514e-01 3.724882e-01 -#> [186] 3.228811e-01 6.624500e-01 8.126232e-01 5.463096e-01 9.512261e-01 -#> [191] 4.814837e-01 5.301889e-01 2.147525e-01 6.535847e-01 2.559981e-01 -#> [196] 3.579175e-01 8.283286e-01 8.870790e-01 8.341937e-01 5.903904e-01 -#> [201] 4.807299e-01 8.526493e-01 8.255190e-01 2.282090e-01 1.320756e-01 -#> [206] 7.775126e-01 6.283700e-01 5.481352e-01 9.123231e-01 6.748970e-01 -#> [211] 2.689369e-01 3.319067e-01 8.463019e-01 7.424585e-01 8.283626e-01 -#> [216] 6.119915e-01 4.210478e-01 4.769737e-01 4.135918e-01 2.903747e-01 -#> [221] 9.279669e-01 1.832669e-02 3.997622e-01 4.360610e-01 6.157701e-01 -#> [226] 6.775670e-01 9.367123e-01 2.842308e-01 4.739750e-01 2.813141e-01 -#> [231] 4.553210e-01 7.070964e-01 7.987352e-01 7.299530e-01 3.025411e-01 -#> [236] 9.069150e-01 9.608043e-01 8.180575e-01 5.125825e-01 6.650703e-02 -#> [241] 1.718663e-01 4.635191e-01 8.976720e-01 2.922489e-01 1.300253e-01 -#> [246] 5.460797e-01 6.306756e-01 8.098946e-01 2.642022e-01 7.639864e-01 -#> [251] 2.931063e-01 5.775031e-01 7.860199e-01 3.518381e-01 2.794586e-01 -#> [256] 2.858959e-01 8.276341e-01 9.808762e-01 9.996882e-01 4.336880e-01 -#> [261] 9.485243e-01 4.278432e-01 1.034282e-01 4.728999e-01 1.727999e-01 -#> [266] 7.037375e-02 4.156002e-01 7.386727e-02 2.945748e-02 9.365961e-01 -#> [271] 3.764979e-01 4.965403e-01 1.908080e-01 8.787847e-01 9.697081e-01 -#> [276] 5.137319e-01 6.952720e-01 1.381933e-01 6.195187e-02 1.863377e-01 -#> [281] 6.696049e-01 7.530222e-01 6.653448e-01 6.788227e-01 6.857185e-01 -#> [286] 5.410656e-01 6.399272e-01 4.589897e-01 4.850110e-01 9.146477e-01 -#> [291] 8.445714e-01 3.214657e-01 1.510498e-01 8.928313e-01 7.094392e-01 -#> [296] 5.331179e-01 7.514957e-01 2.164223e-01 8.920378e-01 8.928208e-02 -#> [301] 3.631122e-01 8.404453e-01 3.431239e-02 1.389114e-02 6.617135e-01 -#> [306] 8.001245e-01 9.449664e-01 7.558392e-01 7.800364e-01 2.303142e-02 -#> [311] 7.833009e-01 1.940282e-01 9.266794e-01 2.013589e-01 3.289097e-01 -#> [316] 3.948048e-02 7.211418e-01 6.137407e-01 9.435936e-01 7.313730e-01 -#> [321] 2.006082e-01 6.831126e-01 5.633407e-01 6.980575e-01 1.107408e-01 -#> [326] 1.195294e-01 3.272125e-01 9.111995e-02 3.833568e-01 2.031279e-01 -#> [331] 7.020209e-01 3.549751e-01 4.287367e-01 1.339121e-02 4.483916e-02 -#> [336] 6.283449e-01 5.391445e-01 9.575830e-01 1.552065e-01 6.634129e-01 -#> [341] 1.577134e-01 7.916594e-02 9.987645e-01 9.143786e-01 2.176331e-01 -#> [346] 3.867223e-01 2.338364e-01 1.107013e-01 3.703267e-01 4.761017e-01 -#> [351] 3.593191e-02 4.432781e-01 3.788068e-01 1.830582e-01 7.605679e-01 -#> [356] 1.295962e-01 4.877590e-01 6.653828e-01 3.868824e-01 1.713247e-01 -#> [361] 8.742815e-01 4.473795e-01 4.692181e-01 5.478841e-01 7.072362e-02 -#> [366] 4.864522e-01 1.644903e-01 8.619222e-01 4.230570e-01 1.670347e-01 -#> [371] 5.481141e-01 9.955785e-01 5.022949e-01 4.363372e-01 7.205906e-01 -#> [376] 2.112372e-01 5.188457e-01 4.617394e-01 6.250282e-01 6.960037e-01 -#> [381] 4.014993e-01 4.466227e-01 5.207871e-01 2.781201e-01 6.753447e-01 -#> [386] 4.572756e-01 3.490790e-01 2.479615e-01 3.402127e-01 1.582112e-01 -#> [391] 1.992836e-01 4.415896e-01 4.133930e-01 9.441801e-01 5.975012e-01 -#> [396] 4.854102e-01 7.633120e-01 2.977414e-01 4.622998e-01 7.335177e-01 -#> [401] 8.054686e-01 2.234338e-01 2.553034e-01 9.160890e-01 6.232499e-01 -#> [406] 9.899361e-01 4.083644e-01 6.087581e-01 5.210107e-01 6.377686e-01 -#> [411] 7.958881e-01 7.464691e-01 4.952654e-01 4.611044e-01 5.340745e-01 -#> [416] 3.303502e-01 4.747677e-01 1.620419e-01 4.709747e-01 6.509053e-01 -#> [421] 3.154967e-01 5.631926e-01 5.118057e-01 3.410325e-01 8.158386e-01 -#> [426] 5.948009e-01 7.715316e-01 3.471733e-01 4.128610e-01 2.112068e-01 -#> [431] 7.411379e-01 8.996246e-01 8.957563e-01 4.693744e-01 6.585784e-01 -#> [436] 6.894635e-01 3.937343e-01 5.424866e-01 4.330502e-01 3.417384e-01 -#> [441] 7.161468e-01 9.156758e-01 4.081541e-01 3.362508e-01 3.528603e-01 -#> [446] 1.690117e-01 5.061618e-01 9.243871e-01 8.758714e-01 4.997471e-01 -#> [451] 3.092422e-01 9.628350e-01 6.415034e-01 8.646630e-01 4.526095e-01 -#> [456] 4.557355e-02 4.631753e-01 2.065046e-01 7.361521e-01 5.369416e-01 -#> [461] 4.882243e-01 2.633679e-01 4.050061e-01 1.789975e-01 5.493113e-01 -#> [466] 8.915581e-01 3.067863e-01 3.350031e-01 9.830739e-01 8.313372e-01 -#> [471] 6.844965e-01 7.854408e-01 2.550006e-02 7.379854e-01 1.527453e-01 -#> [476] 4.423608e-01 2.386506e-01 2.840459e-01 9.602914e-01 3.141736e-01 -#> [481] 7.620242e-01 8.501982e-02 4.570668e-02 5.319074e-02 7.071177e-01 -#> [486] 7.765477e-01 3.632199e-01 2.993536e-01 5.237889e-01 7.598125e-01 -#> [491] 5.102885e-01 6.536787e-01 1.700186e-01 5.224210e-01 4.596340e-01 -#> [496] 7.963172e-01 9.019029e-01 4.303389e-01 9.695532e-01 3.504947e-01 -#> [501] 4.615124e-01 2.473633e-01 3.610598e-01 4.826241e-01 3.911701e-01 -#> [506] 2.916431e-01 6.819670e-01 8.374387e-01 9.779651e-01 1.158332e-01 -#> [511] 6.159596e-01 4.163163e-02 1.539914e-01 8.937990e-01 4.234580e-01 -#> [516] 4.936732e-01 2.465533e-01 1.490410e-01 1.110573e-01 5.564417e-01 -#> [521] 2.345601e-01 5.333389e-01 8.535397e-01 4.120595e-01 5.531162e-02 -#> [526] 8.821365e-01 7.913602e-01 1.996799e-01 2.788708e-01 7.574727e-01 -#> [531] 6.128369e-01 2.089941e-01 7.225543e-01 4.815936e-01 3.745438e-01 -#> [536] 9.423399e-02 6.440581e-01 7.649582e-01 5.066363e-01 4.380851e-01 -#> [541] 3.803321e-01 8.994935e-01 9.246082e-01 7.960675e-01 9.562377e-01 -#> [546] 7.165446e-02 6.881931e-01 7.994153e-02 2.335582e-01 3.574490e-01 -#> [551] 5.061341e-01 2.461889e-01 6.849919e-01 4.076003e-01 2.670269e-01 -#> [556] 3.445565e-01 3.868300e-02 4.786485e-01 4.449749e-01 7.072325e-01 -#> [561] 4.052631e-01 3.537385e-01 9.518808e-01 5.120865e-01 5.285303e-02 -#> [566] 2.276023e-01 9.093051e-02 5.840847e-01 2.805994e-01 7.494842e-01 -#> [571] 7.948750e-01 4.009180e-01 2.536475e-01 3.429767e-01 8.129814e-01 -#> [576] 7.601357e-01 3.148778e-01 9.592469e-01 5.833319e-01 2.652770e-01 -#> [581] 2.219438e-01 9.245375e-01 4.262057e-01 1.630280e-01 9.410540e-01 -#> [586] 7.744225e-01 7.274429e-01 5.580903e-01 8.766353e-03 6.459315e-01 -#> [591] 2.764929e-01 1.294499e-01 6.040567e-01 2.577682e-01 5.204191e-01 -#> [596] 3.081575e-01 7.505825e-01 9.031959e-02 5.839333e-01 3.590320e-01 -#> [601] 1.874069e-01 8.524652e-01 7.411829e-01 1.319659e-01 7.302772e-01 -#> [606] 7.280401e-01 2.674485e-01 7.396386e-01 9.937811e-01 9.158532e-01 -#> [611] 2.232870e-01 6.583251e-01 2.277784e-01 1.099660e-01 9.565532e-01 -#> [616] 3.431873e-01 2.776316e-01 7.077424e-01 6.866407e-01 3.550673e-01 -#> [621] 5.614724e-01 7.994747e-01 1.669566e-01 8.679313e-01 7.465212e-01 -#> [626] 1.003564e-01 8.911707e-02 4.061405e-01 2.867851e-01 1.246053e-01 -#> [631] 7.561402e-01 7.182768e-01 1.520255e-01 1.809036e-01 4.851927e-01 -#> [636] 5.845586e-01 2.063947e-01 8.341374e-01 5.862348e-01 7.336161e-01 -#> [641] 1.374030e-01 1.552088e-01 6.063288e-01 8.881050e-02 6.614613e-01 -#> [646] 1.431773e-01 1.522665e-01 8.191383e-02 3.834797e-01 1.024153e-01 -#> [651] 8.804530e-01 4.254374e-01 7.842035e-01 3.511975e-01 3.494609e-01 -#> [656] 8.933644e-01 8.948860e-01 3.084192e-01 5.520539e-02 7.705742e-01 -#> [661] 4.557562e-01 2.370450e-01 5.866579e-01 9.815024e-01 5.635302e-01 -#> [666] 1.913195e-01 6.683031e-01 2.880332e-01 2.371995e-01 2.315970e-01 -#> [671] 1.993410e-01 1.932464e-01 4.416243e-01 4.558328e-01 7.511110e-01 -#> [676] 2.749461e-01 6.875317e-01 6.128225e-02 5.488885e-01 5.439873e-01 -#> [681] 2.764143e-01 3.475451e-01 3.048136e-01 2.079821e-01 8.466981e-01 -#> [686] 9.827144e-01 4.261723e-01 9.476098e-01 1.275649e-01 2.665210e-01 -#> [691] 8.841565e-01 8.692216e-01 5.900482e-01 4.717168e-01 9.482428e-01 -#> [696] 4.437333e-01 6.280763e-01 1.219550e-01 1.409143e-01 6.966829e-01 -#> [701] 6.145782e-01 2.848213e-01 3.618627e-01 2.321316e-01 4.196723e-01 -#> [706] 6.494500e-01 3.654670e-02 2.642884e-03 4.594015e-01 1.871041e-01 -#> [711] 1.237204e-01 2.172277e-02 5.862153e-01 5.654604e-01 9.932829e-01 -#> [716] 8.778479e-01 1.533280e-01 2.888981e-01 1.125810e-01 2.000958e-02 -#> [721] 3.623547e-02 1.867395e-01 6.006737e-01 9.894985e-01 4.605974e-01 -#> [726] 6.587709e-01 2.150734e-01 3.918479e-01 1.736656e-01 1.165350e-01 -#> [731] 1.806955e-02 3.659735e-01 7.655495e-01 1.575079e-01 6.598505e-01 -#> [736] 9.331903e-01 4.297725e-01 7.280043e-01 1.573318e-01 2.461837e-01 -#> [741] 5.149574e-01 5.810841e-01 9.618195e-01 8.502707e-01 5.955745e-01 -#> [746] 4.676673e-01 2.109651e-02 6.822403e-01 1.910610e-01 6.879974e-01 -#> [751] 1.417310e-01 4.184667e-01 8.748336e-01 5.160320e-01 7.127919e-01 -#> [756] 1.862157e-01 1.671759e-01 2.433068e-02 1.311244e-02 4.936894e-01 -#> [761] 1.920213e-01 9.428024e-01 7.758707e-01 9.824188e-01 1.203631e-01 -#> [766] 9.528757e-01 4.073304e-01 3.272850e-03 2.256920e-02 4.097970e-01 -#> [771] 1.725599e-01 9.593439e-01 3.480026e-01 7.547643e-01 2.418426e-01 -#> [776] 3.505656e-01 1.779432e-01 6.054327e-01 4.133119e-01 2.426442e-01 -#> [781] 6.122967e-01 4.817739e-01 5.778852e-01 1.751137e-01 4.959224e-01 -#> [786] 4.855521e-01 4.288694e-01 3.272740e-01 7.126763e-01 5.941206e-01 -#> [791] 7.173923e-01 8.479271e-01 2.064803e-01 7.677652e-01 8.408466e-01 -#> [796] 5.262039e-01 6.567142e-01 8.289853e-02 1.150261e-01 5.744440e-01 -#> [801] 1.078779e-01 3.645713e-01 1.919978e-01 5.945217e-01 9.356417e-01 -#> [806] 1.751562e-01 5.315525e-01 4.630100e-02 7.443600e-01 9.536151e-01 -#> [811] 9.886818e-01 6.377355e-01 6.354429e-01 9.632055e-01 3.359300e-01 -#> [816] 9.341318e-01 5.478250e-01 1.377514e-01 6.934627e-01 4.422727e-01 -#> [821] 2.779436e-01 2.003882e-01 4.374240e-01 2.722941e-01 3.420865e-01 -#> [826] 1.963684e-01 6.465580e-01 3.878812e-01 8.827484e-01 8.984859e-02 -#> [831] 4.495634e-01 4.791352e-01 2.018548e-01 9.893510e-01 6.971420e-01 -#> [836] 1.480124e-01 7.080017e-01 9.599538e-01 4.051585e-01 1.035957e-01 -#> [841] 7.152330e-01 2.236661e-01 4.444888e-01 3.434944e-01 2.536357e-01 -#> [846] 5.178003e-01 2.484090e-01 2.815200e-01 5.262293e-01 4.090020e-01 -#> [851] 5.698297e-05 7.668141e-03 3.975573e-01 3.351346e-01 4.022110e-01 -#> [856] 6.165786e-01 5.729289e-01 5.933223e-01 2.306403e-01 1.442407e-01 -#> [861] 2.009472e-01 4.943279e-01 1.005442e-01 4.408993e-01 1.320863e-01 -#> [866] 6.449211e-01 9.850494e-01 6.296212e-01 6.100809e-01 6.300376e-01 -#> [871] 6.450246e-01 7.049011e-01 3.018348e-01 6.925567e-01 9.512587e-01 -#> [876] 2.518367e-02 1.444711e-01 5.349564e-01 1.018160e-01 7.005942e-01 -#> [881] 9.361693e-01 4.197982e-01 5.722439e-01 8.617896e-01 8.946732e-01 -#> [886] 4.492323e-01 4.751024e-02 5.285338e-01 3.755010e-03 1.753946e-01 -#> [891] 9.503928e-01 9.425190e-01 5.091777e-01 1.793649e-01 9.564283e-01 -#> [896] 6.000894e-01 5.678489e-03 4.402577e-01 4.999100e-01 7.901656e-01 -#> [901] 8.285700e-01 6.220512e-01 7.525185e-01 9.808566e-01 3.031627e-01 -#> [906] 3.638969e-01 5.737774e-01 7.974222e-01 1.927143e-01 7.096579e-02 -#> [911] 6.637665e-01 5.325533e-01 2.753842e-01 1.657288e-02 8.505290e-01 -#> [916] 3.544237e-01 8.951357e-01 7.594585e-01 7.929092e-01 3.690021e-01 -#> [921] 9.885443e-01 5.202596e-01 4.816507e-01 5.603812e-01 4.059491e-01 -#> [926] 1.780772e-01 2.555985e-01 9.527670e-01 9.492342e-01 2.503465e-01 -#> [931] 4.463720e-01 2.528919e-01 1.102649e-01 1.164325e-01 4.280339e-01 -#> [936] 1.354578e-01 9.509876e-01 5.564700e-01 5.596629e-01 4.858069e-01 -#> [941] 7.061451e-01 4.799485e-01 1.143938e-01 5.256956e-01 4.923019e-01 -#> [946] 6.756639e-01 8.019810e-01 5.067972e-02 2.507613e-01 4.069437e-01 -#> [951] 3.276303e-01 2.237825e-01 9.002859e-01 7.538226e-01 2.925664e-01 -#> [956] 2.633689e-01 4.925530e-01 5.501800e-01 4.931809e-01 2.187330e-01 -#> [961] 2.136674e-01 1.284627e-01 3.190255e-02 7.759703e-01 6.836006e-01 -#> [966] 4.023029e-02 5.471501e-01 9.166965e-01 6.651135e-01 2.377981e-01 -#> [971] 7.333021e-01 2.663977e-01 1.874515e-01 1.774807e-01 2.519407e-01 -#> [976] 7.279319e-01 2.723705e-01 5.014268e-01 6.650865e-01 2.305334e-01 -#> [981] 1.905749e-01 9.799571e-01 2.735355e-01 4.756708e-01 9.019580e-01 -#> [986] 9.228311e-01 3.872787e-01 6.981417e-01 6.761298e-01 7.024149e-01 -#> [991] 5.735192e-01 8.711005e-01 4.285600e-01 4.692609e-01 4.832521e-01 -#> [996] 3.575448e-01 3.148074e-01 6.405638e-01 2.450572e-01 5.444350e-01 -#> [1001] 1.345300e-01 8.788860e-01 6.500524e-01 4.292569e-01 3.451318e-01 -#> [1006] 7.908153e-01 5.535534e-01 4.987910e-02 3.291545e-01 2.536093e-02 -#> [1011] 9.957070e-01 8.555239e-01 1.408815e-01 4.431854e-01 2.354612e-01 -#> [1016] 6.397074e-01 4.949633e-01 2.505278e-02 4.825873e-01 9.331015e-01 -#> [1021] 4.125940e-01 9.420214e-01 3.686829e-01 9.539024e-01 1.055071e-01 -#> [1026] 4.296699e-01 2.853285e-01 5.591850e-01 2.830951e-01 6.670140e-01 -#> [1031] 2.007128e-01 9.397887e-01 1.203406e-01 4.366358e-01 3.730674e-01 -#> [1036] 2.620464e-01 3.042087e-01 8.369897e-02 1.996781e-01 6.088287e-01 -#> [1041] 4.238849e-02 3.726618e-01 8.133340e-02 6.947755e-01 9.492405e-01 -#> [1046] 4.260592e-01 3.987327e-01 3.779399e-01 7.706273e-01 1.057720e-01 -#> [1051] 4.523877e-01 5.531511e-01 7.217947e-01 4.553711e-01 4.735801e-01 -#> [1056] 7.176209e-01 8.148502e-01 8.167231e-01 7.890259e-01 9.493617e-01 -#> [1061] 2.648982e-01 8.503215e-01 1.677853e-01 6.148393e-01 8.903800e-01 -#> [1066] 3.688923e-01 1.257008e-01 7.099451e-01 6.389231e-01 8.532737e-01 -#> [1071] 2.958283e-01 2.291272e-01 4.003309e-01 6.055816e-01 3.764217e-01 -#> [1076] 5.560982e-01 6.447780e-01 7.082342e-01 5.132301e-01 1.257772e-01 -#> [1081] 6.029584e-01 8.348644e-01 3.884209e-01 1.178496e-01 8.579102e-02 -#> [1086] 4.602041e-01 9.649266e-01 5.448183e-02 8.509911e-01 4.747059e-01 -#> [1091] 8.797902e-01 1.578948e-01 9.263599e-01 7.144946e-01 3.466359e-01 -#> [1096] 2.263795e-02 7.028324e-01 2.026552e-01 6.876447e-01 6.461817e-01 -#> [1101] 2.402308e-02 1.257378e-01 4.392930e-01 5.703774e-01 6.898211e-01 -#> [1106] 7.362020e-01 3.174739e-01 6.056084e-01 6.166393e-01 3.041729e-01 -#> [1111] 2.765572e-01 5.816801e-01 7.028831e-01 1.089807e-01 1.806387e-01 -#> [1116] 7.162778e-01 4.613546e-01 8.290836e-02 1.161752e-01 4.343853e-01 -#> [1121] 4.051397e-01 9.699104e-01 4.344835e-01 1.131182e-01 6.784924e-01 -#> [1126] 7.669101e-01 6.090446e-01 1.205942e-01 7.493839e-01 8.279801e-01 -#> [1131] 8.581206e-01 1.756258e-01 4.064683e-01 3.443180e-01 2.782962e-01 -#> [1136] 2.433467e-01 6.704846e-01 1.636397e-01 7.818128e-01 6.331869e-01 -#> [1141] 7.545399e-01 5.644823e-01 2.052246e-01 8.996652e-01 4.418509e-01 -#> [1146] 5.989642e-02 7.166131e-01 2.904225e-01 8.021183e-01 2.575020e-01 -#> [1151] 1.338957e-01 6.692374e-01 4.720811e-02 6.985869e-01 9.960922e-01 -#> [1156] 9.433979e-01 8.096795e-01 6.483186e-01 -#> -#> $hfunc2 -#> [1] 0.3602979339 0.3868530518 0.3659582292 0.6115207085 0.2979329665 -#> [6] 0.3048357560 0.3438431596 0.6518987137 0.6759897327 0.5547543918 -#> [11] 0.7331852854 0.9573768084 0.3507158679 0.2271521321 0.4020598129 -#> [16] 0.1810535670 0.6723651456 0.8985834539 0.2899298765 0.7204078959 -#> [21] 0.8501991653 0.4603316335 0.4192033381 0.9035938396 0.3615789034 -#> [26] 0.8251909389 0.9015912998 0.4367673416 0.7768123279 0.6203341800 -#> [31] 0.8596998393 0.4823129859 0.7061346845 0.9661257295 0.2500766630 -#> [36] 0.1228342604 0.3847923381 0.2864047692 0.5591397824 0.5677644633 -#> [41] 0.5679038484 0.2036819050 0.4195141707 0.9417793863 0.9203375621 -#> [46] 0.0169195564 0.4676558520 0.1381660940 0.0955139203 0.2523360718 -#> [51] 0.6005016667 0.1129944966 0.4177456511 0.2676088504 0.3327203723 -#> [56] 0.7950253109 0.8032401035 0.0446320259 0.4423884961 0.1230002250 -#> [61] 0.9146304872 0.8457945510 0.5227954517 0.8208220753 0.9092193046 -#> [66] 0.3542929477 0.4994377786 0.2601389222 0.2787378942 0.0120041378 -#> [71] 0.0327136044 0.1643138824 0.2395915278 0.9395575810 0.5173032062 -#> [76] 0.1789059161 0.6667914257 0.6751221222 0.5117736571 0.0528298852 -#> [81] 0.6026595227 0.0047418302 0.7309208537 0.6984327991 0.4686162333 -#> [86] 0.7567127664 0.7501808344 0.4501390535 0.7582690871 0.4885938070 -#> [91] 0.5893851583 0.0667709599 0.2880634034 0.2563626521 0.9402382812 -#> [96] 0.6569588202 0.6650528986 0.6989046736 0.8506293968 0.5476785717 -#> [101] 0.2823542360 0.5648867364 0.6595557701 0.1777972296 0.9509426855 -#> [106] 0.8269240666 0.4160782714 0.7448737647 0.6480376966 0.5092542214 -#> [111] 0.3390633400 0.7734589863 0.6329463011 0.4977176240 0.2863894441 -#> [116] 0.6835141830 0.6851087313 0.2440155461 0.3249232074 0.1906817549 -#> [121] 0.6674449639 0.0407809497 0.6825629177 0.8988593743 0.0464068345 -#> [126] 0.6778086462 0.8534700941 0.3786195945 0.1017327545 0.0491179839 -#> [131] 0.2155701292 0.6155730420 0.8210330787 0.4902426466 0.7756693928 -#> [136] 0.8551385252 0.2981655266 0.4974218833 0.9535755396 0.3808937537 -#> [141] 0.7188332162 0.2160509561 0.3543044306 0.2367622555 0.1178228716 -#> [146] 0.9681445209 0.5775578047 0.4183000484 0.8888511047 0.4590290731 -#> [151] 0.1443458689 0.2093322480 0.5906135398 0.5555647895 0.1265074870 -#> [156] 0.5979861729 0.1673470395 0.3761195295 0.0162187976 0.8828100773 -#> [161] 0.2735453103 0.8127120867 0.6193409711 0.5659049280 0.4306097010 -#> [166] 0.2860994456 0.1896105425 0.7896646138 0.3843820601 0.4332293785 -#> [171] 0.9613750039 0.8413304282 0.6767389183 0.7500778055 0.5829413150 -#> [176] 0.4103787344 0.5949955037 0.9948018742 0.0577988335 0.4237377215 -#> [181] 0.2272214490 0.8628283510 0.3328963264 0.7243015170 0.0577289559 -#> [186] 0.2905064587 0.7226484719 0.9433995271 0.2371001645 0.5947713631 -#> [191] 0.3695327696 0.8349600403 0.9509226820 0.6393767843 0.2643275335 -#> [196] 0.2419421591 0.3649591836 0.4487147695 0.1403573260 0.1071021698 -#> [201] 0.3626918819 0.2446407682 0.0667739427 0.5316676562 0.2297615266 -#> [206] 0.4496800073 0.1249245349 0.9329577781 0.0436974010 0.6279426198 -#> [211] 0.1071748278 0.7266188763 0.7805709719 0.2974466657 0.0904944480 -#> [216] 0.5514406179 0.2853423208 0.8067490394 0.3206238836 0.8537749263 -#> [221] 0.0848937579 0.9946752463 0.6321050810 0.7148637608 0.1642317572 -#> [226] 0.4619152540 0.2748352932 0.8794597591 0.5396498932 0.7253746363 -#> [231] 0.6154912821 0.4326914907 0.1751363451 0.4706118920 0.5470187902 -#> [236] 0.8112137096 0.2099073035 0.0863107290 0.5831665383 0.3950011504 -#> [241] 0.7776498489 0.4876754553 0.1286191136 0.5101264691 0.8045023610 -#> [246] 0.6486328274 0.9398062316 0.1018205001 0.7460307181 0.7348691560 -#> [251] 0.5064798715 0.5169620235 0.4256382861 0.5292969747 0.7308173507 -#> [256] 0.2048741271 0.3616677608 0.0050638761 0.0013326298 0.7708307269 -#> [261] 0.1008532406 0.2770715943 0.3850523754 0.8608938053 0.7669598258 -#> [266] 0.3673760390 0.8952888963 0.8037299760 0.6963857621 0.0562156324 -#> [271] 0.1028489610 0.5774010285 0.5501989469 0.7374746850 0.1182938303 -#> [276] 0.9614141163 0.1420394930 0.9741156100 0.9327547295 0.2123848575 -#> [281] 0.4352987534 0.3102848339 0.3916455436 0.1420868061 0.7015310820 -#> [286] 0.1344012104 0.4547926493 0.6884877611 0.1483746384 0.2428354218 -#> [291] 0.0851547444 0.5644857563 0.7232497365 0.3266771371 0.2715090207 -#> [296] 0.7796778607 0.7087958528 0.1554253588 0.5784324259 0.4653117013 -#> [301] 0.0878993633 0.0803192335 0.9571207312 0.7930953199 0.5906062147 -#> [306] 0.4769853523 0.0685989330 0.4300242324 0.4659937234 0.9702490197 -#> [311] 0.0758323256 0.9187733204 0.1486959878 0.9215475999 0.7052425570 -#> [316] 0.9980161456 0.0431242355 0.2569793271 0.2245581775 0.7668679047 -#> [321] 0.3501016136 0.5912576939 0.2701534475 0.1818662875 0.7835187379 -#> [326] 0.2856799446 0.7783974304 0.4724987686 0.4432145800 0.9102631696 -#> [331] 0.4455895222 0.9397466013 0.9882458539 0.9965969183 0.7839831934 -#> [336] 0.1556048523 0.6392752197 0.0493086385 0.5654789962 0.7010460895 -#> [341] 0.2069559137 0.9809612969 0.0349085349 0.0779248391 0.8713032278 -#> [346] 0.1850185587 0.6872387354 0.1630232149 0.3177454077 0.4227788509 -#> [351] 0.1744492535 0.5745326282 0.6302465667 0.1592283391 0.8014001460 -#> [356] 0.4614678591 0.8945579853 0.5654828447 0.3873400426 0.1894393848 -#> [361] 0.4233942424 0.4061521551 0.4731583391 0.2820430185 0.5458941837 -#> [366] 0.6799183279 0.0995542211 0.3701869870 0.1297803734 0.3119399001 -#> [371] 0.5314272674 0.1506127888 0.7431659566 0.6691214186 0.4843078337 -#> [376] 0.7225475275 0.3855944359 0.1982962225 0.3013871560 0.9563619365 -#> [381] 0.8879615470 0.7334661063 0.6220295111 0.1212285255 0.4902726218 -#> [386] 0.4911635004 0.7329098237 0.3213473728 0.7586615109 0.2600967959 -#> [391] 0.1687731467 0.5446438317 0.5109694447 0.6705053239 0.4377042097 -#> [396] 0.2190664394 0.8098991513 0.5728313548 0.7429565783 0.4427041490 -#> [401] 0.1480158293 0.7887705839 0.2818338689 0.2159913462 0.2720364551 -#> [406] 0.2815133582 0.0797820683 0.4188362262 0.8713283209 0.0835803022 -#> [411] 0.3557827744 0.5080137997 0.8370868197 0.5705359119 0.7693541461 -#> [416] 0.6043845820 0.2719652378 0.6842337032 0.2334529900 0.7640014832 -#> [421] 0.7563851005 0.7042253996 0.3500132756 0.9223013211 0.1158699656 -#> [426] 0.6185513190 0.4981221606 0.3549103254 0.0448196200 0.3377840055 -#> [431] 0.6026228025 0.1379617594 0.3555165811 0.4848435932 0.0601014498 -#> [436] 0.3975567071 0.2979412140 0.5249596146 0.8983687274 0.1834426539 -#> [441] 0.3712017072 0.6347900718 0.6578412735 0.3052217775 0.6886412094 -#> [446] 0.9057192566 0.3897147760 0.6710112965 0.4495019431 0.4177674849 -#> [451] 0.8187897559 0.2593676213 0.6791004975 0.2099329507 0.5852895011 -#> [456] 0.3430087436 0.9454782615 0.7057257494 0.6387367497 0.7697376988 -#> [461] 0.4621322739 0.6640648067 0.9306947637 0.8465153269 0.5031780701 -#> [466] 0.0780049660 0.1904604244 0.2499423742 0.4357465304 0.4410980320 -#> [471] 0.5744816258 0.3849706033 0.9958558135 0.2809152672 0.8995707277 -#> [476] 0.6082616490 0.4515398378 0.6267765211 0.0474084928 0.7406932068 -#> [481] 0.2650152900 0.9935728819 0.3760378594 0.2138039256 0.5045585897 -#> [486] 0.6024735204 0.2819947243 0.2696117674 0.6972424435 0.7310827547 -#> [491] 0.5271869229 0.5261184353 0.7807975922 0.4588799159 0.6541953664 -#> [496] 0.4874196188 0.2331075190 0.9091879778 0.1478415459 0.2721218344 -#> [501] 0.9593452451 0.6445315895 0.2570972752 0.9212444825 0.5562163780 -#> [506] 0.3968182416 0.7999913234 0.1651185324 0.0197905910 0.4681236149 -#> [511] 0.3186847983 0.9174216138 0.1190689090 0.5701578212 0.8195153837 -#> [516] 0.6314311538 0.6079594275 0.6910700713 0.3425548365 0.5852047394 -#> [521] 0.2371454897 0.2494527527 0.5702427898 0.1502267298 0.7660293524 -#> [526] 0.6484564570 0.4440694789 0.9315106979 0.9820654229 0.3250201945 -#> [531] 0.3580767260 0.9564966144 0.3361563328 0.2837581489 0.8207083975 -#> [536] 0.5099573514 0.5481498417 0.4150289830 0.3323853001 0.2632225695 -#> [541] 0.4773000822 0.1419845900 0.9917787986 0.1713372742 0.4012782196 -#> [546] 0.2283306405 0.1712470170 0.6998318501 0.6689217315 0.3366585054 -#> [551] 0.7726896682 0.8373391332 0.5326914955 0.6122537637 0.6742242959 -#> [556] 0.1451321126 0.2067799555 0.8819340022 0.3022965728 0.6843682831 -#> [561] 0.7073954719 0.5808120353 0.5828749702 0.3505242929 0.9206796824 -#> [566] 0.9565310104 0.9211499208 0.8013813942 0.7440514274 0.3173967289 -#> [571] 0.5934856556 0.7875299366 0.8627221595 0.8443053733 0.1017885647 -#> [576] 0.2031863013 0.9883196347 0.5881294299 0.2529065440 0.3676572059 -#> [581] 0.5062390399 0.4160138111 0.3694870508 0.5450923117 0.1343427662 -#> [586] 0.1345839783 0.2586427552 0.3399446211 0.9498602200 0.6175089988 -#> [591] 0.6841834814 0.3828409457 0.5144211889 0.3852818459 0.5603676550 -#> [596] 0.6138703117 0.6119633021 0.7530404711 0.4131433503 0.9742692989 -#> [601] 0.9483571101 0.2894445700 0.1300378616 0.6541669915 0.4888190918 -#> [606] 0.2008041341 0.3637642277 0.9442322833 0.1787967663 0.1649434444 -#> [611] 0.6286538402 0.0015834919 0.2518212470 0.6587865058 0.5380582721 -#> [616] 0.5939064961 0.4491298789 0.7835408055 0.9233006198 0.9031842325 -#> [621] 0.5970617738 0.7033117325 0.2852440792 0.2814720887 0.1685589830 -#> [626] 0.4954628965 0.7008137047 0.9279244358 0.9544190104 0.4425845903 -#> [631] 0.6778145472 0.3269640337 0.4932159378 0.9544095654 0.6187518627 -#> [636] 0.0628787703 0.3834242498 0.6092924949 0.8322686591 0.4273459350 -#> [641] 0.7435800262 0.2520850956 0.6524576421 0.4591370391 0.4925247851 -#> [646] 0.2250845442 0.3388182436 0.5161007119 0.0781148254 0.9714643358 -#> [651] 0.6103408978 0.1117112335 0.5063627616 0.1420287424 0.8888880489 -#> [656] 0.3533968613 0.3102264245 0.0786184052 0.7450230880 0.7783252962 -#> [661] 0.1762540205 0.6645075079 0.0891146349 0.1385400393 0.5965295990 -#> [666] 0.9193356789 0.4374766894 0.6810049571 0.6252272225 0.7432358371 -#> [671] 0.5542695684 0.9133417890 0.8731864268 0.7981255798 0.6538209866 -#> [676] 0.0817422474 0.3776380069 0.3047958308 0.1279130689 0.6637773741 -#> [681] 0.5315741689 0.7751062983 0.4770269016 0.7720777393 0.6988783672 -#> [686] 0.5385293745 0.4502497149 0.1572084089 0.9313229601 0.7383589875 -#> [691] 0.0631670850 0.4117803253 0.3852160276 0.5463312029 0.0134753756 -#> [696] 0.4350046018 0.2752307041 0.9098316454 0.9335615102 0.1058721986 -#> [701] 0.1647209640 0.5465460682 0.7126085574 0.3768164001 0.6399556314 -#> [706] 0.6575854322 0.6735478428 0.9897076150 0.1195294778 0.9380343948 -#> [711] 0.3828268882 0.9936176498 0.5356377855 0.6125700280 0.0007258805 -#> [716] 0.1664341622 0.1083716059 0.5326668141 0.6990299332 0.9479788512 -#> [721] 0.8774657694 0.4163648637 0.2464681604 0.0100767851 0.7491120895 -#> [726] 0.6081333149 0.1248321647 0.2581851166 0.0685509851 0.9930060703 -#> [731] 0.9199901938 0.7954498012 0.3425936113 0.4908804482 0.1603113184 -#> [736] 0.7914049681 0.6858096896 0.5085608840 0.6278597448 0.5891867459 -#> [741] 0.8817490070 0.5464230752 0.2644109083 0.1397528062 0.5020074870 -#> [746] 0.8469771376 0.8945431646 0.3057523803 0.3135583532 0.4446068513 -#> [751] 0.8135067220 0.7774050228 0.8859211917 0.6286733542 0.3086519804 -#> [756] 0.4961253740 0.8344396645 0.9219217323 0.9957776294 0.4093742273 -#> [761] 0.8526333125 0.0001640302 0.3490491136 0.0986295370 0.5712219249 -#> [766] 0.0049584063 0.3878337303 0.4362869785 0.0519495000 0.6071585400 -#> [771] 0.1079214016 0.6458289905 0.5431988616 0.2268263762 0.9054858902 -#> [776] 0.5040338242 0.8538869019 0.5469740965 0.4709729113 0.2379225277 -#> [781] 0.5668521191 0.2233239624 0.4110733883 0.6896923724 0.8758725332 -#> [786] 0.5461013774 0.6253623280 0.2328972723 0.6860842092 0.7066716245 -#> [791] 0.1343031000 0.0746949083 0.4545291504 0.4593686761 0.6682778223 -#> [796] 0.4537520604 0.1322659599 0.4269183921 0.2398109065 0.9364632545 -#> [801] 0.6105752293 0.2954731387 0.4752145570 0.8387753714 0.2306671937 -#> [806] 0.5414366051 0.3745781024 0.9848598457 0.2294966299 0.0293642971 -#> [811] 0.5273489347 0.1067626919 0.8431006234 0.0535251226 0.6747745621 -#> [816] 0.6613380361 0.7923559965 0.7454470104 0.3924333155 0.6188390817 -#> [821] 0.6308133565 0.5610336005 0.7780190800 0.2902543493 0.3936265088 -#> [826] 0.9503247082 0.8077370533 0.5853026462 0.7706971858 0.6064350805 -#> [831] 0.1860955249 0.8000675621 0.8528943643 0.0002006685 0.4672945157 -#> [836] 0.7522562741 0.6114568294 0.0772057037 0.7087419993 0.6065628841 -#> [841] 0.2590805111 0.5261388642 0.1423774287 0.7584739633 0.9302268168 -#> [846] 0.4490237304 0.7318116970 0.8915450119 0.6369933654 0.4216906145 -#> [851] 0.9976182685 0.8850415373 0.2327857374 0.7940400213 0.4140635150 -#> [856] 0.8561550590 0.5109281879 0.7739211740 0.2249269682 0.9599012384 -#> [861] 0.6379893604 0.3214197491 0.1662563554 0.3644012959 0.3459957385 -#> [866] 0.7929167368 0.2740586199 0.0849448768 0.7155296516 0.0556240379 -#> [871] 0.3186948700 0.0158202228 0.7784126532 0.2455197531 0.1164226152 -#> [876] 0.5236479456 0.5773258872 0.2702102229 0.3890843112 0.1029379914 -#> [881] 0.1342264223 0.2403077970 0.7915686118 0.0197189976 0.0951981056 -#> [886] 0.3257221502 0.3520683945 0.5563018717 0.7483001523 0.7506170572 -#> [891] 0.4802876791 0.4130999684 0.6216935120 0.9534252759 0.1948125069 -#> [896] 0.0511191561 0.9799752580 0.1637057785 0.5952557538 0.1615089494 -#> [901] 0.0763169687 0.1085469257 0.0962676082 0.2672919289 0.6089525763 -#> [906] 0.4913850119 0.4533114589 0.4447804629 0.8357597600 0.4005345779 -#> [911] 0.3598711731 0.3561619335 0.7444995604 0.7305090066 0.1698977444 -#> [916] 0.1497214184 0.4487057125 0.1428669277 0.5196746762 0.4128227309 -#> [921] 0.0659276833 0.6041693274 0.5205833782 0.8817540999 0.3104817764 -#> [926] 0.0996294498 0.0636116006 0.4134992298 0.0103609680 0.3736973134 -#> [931] 0.4790275062 0.8637950973 0.0311183938 0.1821853932 0.0553248371 -#> [936] 0.2379918657 0.8965856992 0.2075600333 0.5378059980 0.5657839434 -#> [941] 0.6759399069 0.3616786157 0.2011128865 0.5245465558 0.4633659923 -#> [946] 0.0520071299 0.6643116194 0.1949919159 0.4217891441 0.0076760508 -#> [951] 0.6238235883 0.0384178366 0.8728699010 0.5099796345 0.0961255861 -#> [956] 0.1404439938 0.6354482109 0.5397277017 0.5551195377 0.3162814086 -#> [961] 0.5419412871 0.3793455795 0.4022199144 0.9706209384 0.2856490825 -#> [966] 0.9762631572 0.7606160280 0.5626717376 0.1863443606 0.1552142899 -#> [971] 0.5242510271 0.8638923434 0.3721061163 0.4841737192 0.7038044054 -#> [976] 0.4189399800 0.5164203491 0.4547907977 0.0051510140 0.7590672425 -#> [981] 0.4434466707 0.7273803642 0.8077522359 0.3385753969 0.4097195083 -#> [986] 0.2235144778 0.1253816403 0.5574280294 0.2150598766 0.5458425378 -#> [991] 0.1668320943 0.8413062845 0.7423587766 0.7456963661 0.3129147954 -#> [996] 0.3742409623 0.6650375876 0.7711914404 0.6415724541 0.5602540147 -#> [1001] 0.6188156846 0.2124016734 0.3089051399 0.8485943190 0.8742153591 -#> [1006] 0.4067439310 0.3212779474 0.7480535795 0.1424894399 0.8775738500 -#> [1011] 0.0051011732 0.2212391152 0.6238164749 0.0353481381 0.2044880829 -#> [1016] 0.7185622324 0.0788015927 0.8824484977 0.5892186399 0.1306650442 -#> [1021] 0.1007365260 0.5049888087 0.4022016401 0.5823915514 0.9579785082 -#> [1026] 0.1117105292 0.3377216567 0.6468134720 0.9915249303 0.3139406065 -#> [1031] 0.9910919139 0.2687688896 0.2636426345 0.4997814528 0.2095245811 -#> [1036] 0.8092740227 0.5116563266 0.2562519572 0.6419063783 0.3062791384 -#> [1041] 0.2612783727 0.4045980680 0.8530145561 0.1153688835 0.8506425013 -#> [1046] 0.2435012044 0.1485147123 0.4127696220 0.9089896869 0.1934780493 -#> [1051] 0.4908700485 0.4797994594 0.9430511917 0.8263137876 0.7052891438 -#> [1056] 0.3555770606 0.3382903796 0.2013632703 0.1899537720 0.2350227101 -#> [1061] 0.7463738984 0.5877167359 0.7747166861 0.2142283148 0.2290652929 -#> [1066] 0.2860088308 0.0689789055 0.6619440928 0.5744474503 0.9198727571 -#> [1071] 0.9148936865 0.5300326250 0.3395870430 0.4515438576 0.9658781856 -#> [1076] 0.7619702302 0.2427006333 0.3199363239 0.5156448205 0.2502346306 -#> [1081] 0.3460812149 0.6086284737 0.2214564158 0.9824025897 0.8067799183 -#> [1086] 0.2865817951 0.1149667443 0.9977094565 0.4736712233 0.4825431907 -#> [1091] 0.3558017876 0.5099751349 0.5246431754 0.2412751788 0.6697760635 -#> [1096] 0.2786853033 0.1153124940 0.8486932573 0.7794308369 0.6011647077 -#> [1101] 0.9968299241 0.3062592829 0.6249847913 0.4725776085 0.6342648330 -#> [1106] 0.3411507271 0.3286367125 0.3321631536 0.9838202770 0.5953493906 -#> [1111] 0.5557981485 0.2494124446 0.4023704351 0.5113250692 0.6088485060 -#> [1116] 0.5134947308 0.7290613227 0.8074504491 0.2750230223 0.2916297335 -#> [1121] 0.0558592780 0.0776608107 0.5502043781 0.1925702617 0.3470351456 -#> [1126] 0.8257441805 0.1111294624 0.6245933453 0.8866048110 0.0560099033 -#> [1131] 0.6895549189 0.0856778460 0.5612822489 0.5368451961 0.5767791342 -#> [1136] 0.5954236452 0.5543859131 0.6204617325 0.9345829161 0.7434144567 -#> [1141] 0.8912522963 0.6551713275 0.7374149371 0.3752647456 0.8347036744 -#> [1146] 0.9201580009 0.8533951659 0.5439155892 0.1892795168 0.5452197446 -#> [1151] 0.9640701556 0.1469945355 0.9782907595 0.8144351537 0.0263820822 -#> [1156] 0.1861138014 0.1154144500 0.4989536219 -#> # or using the fast versions h1 <- BiCopHfunc1(daxreturns[, 2], daxreturns[, 1], cop) h2 <- BiCopHfunc2(daxreturns[, 2], daxreturns[, 1], cop) @@ -667,15 +198,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopHfuncDeriv.html b/docs/reference/BiCopHfuncDeriv.html index 170b6ab..25c3ecf 100644 --- a/docs/reference/BiCopHfuncDeriv.html +++ b/docs/reference/BiCopHfuncDeriv.html @@ -5,7 +5,7 @@ - +
    @@ -33,14 +33,14 @@
    - +
    @@ -71,13 +71,15 @@

    Derivatives of the h-Function of a Bivariate Copula

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    numeric vectors of equal length with values in \([0,1]\).

    -
    family
    +
    family

    integer; single number or vector of size length(u1); -defines the bivariate copula family: \
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; ``survival Joe'')
    23 = rotated Clayton copula (90 degrees)
    +defines the bivariate copula family: \
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; “survival Joe”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `33` = rotated Clayton copula (270 degrees)
    @@ -85,28 +87,28 @@

    Arguments

    `36` = rotated Joe copula (270 degrees)

    -
    par
    +
    par

    numeric; single number or vector of size length(u1); copula parameter.

    -
    par2
    +
    par2

    integer; single number or vector of size length(u1); second parameter for the t-Copula; default is par2 = 0, should be an positive integer for the Students's t copula family = 2.

    -
    deriv
    +
    deriv

    Derivative argument
    "par" = derivative with respect to the first parameter (default)
    "par2" = derivative with respect to the second parameter (only available for the t-copula)
    "u2" = derivative with respect to the second argument u2

    -
    obj
    +
    obj

    BiCop object containing the family and parameter specification.

    -
    check.pars
    +
    check.pars

    logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

    @@ -114,9 +116,7 @@

    Arguments

    Value

    - - -

    A numeric vector of the conditional bivariate copula derivative

    • of the copula family,

      • +

      A numeric vector of the conditional bivariate copula derivative

      • of the copula family,

      • with parameter(s) par, par2,

      • with respect to deriv,

      • evaluated at u1 and u2.

        • @@ -213,15 +213,15 @@

        Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopHfuncDeriv2.html b/docs/reference/BiCopHfuncDeriv2.html index a742b44..e18f7ed 100644 --- a/docs/reference/BiCopHfuncDeriv2.html +++ b/docs/reference/BiCopHfuncDeriv2.html @@ -5,7 +5,7 @@ - +
    @@ -33,14 +33,14 @@
    - +
    @@ -71,13 +71,15 @@

    Second Derivatives of the h-Function of a Bivariate Copula

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    numeric vectors of equal length with values in \([0,1]\).

    -
    family
    +
    family

    integer; single number or vector of size length(u1); -defines the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; ``survival Joe'')
    23 = rotated Clayton copula (90 degrees)
    +defines the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; “survival Joe”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `33` = rotated Clayton copula (270 degrees)
    @@ -85,18 +87,18 @@

    Arguments

    `36` = rotated Joe copula (270 degrees)

    -
    par
    +
    par

    numeric; single number or vector of size length(u1); copula parameter.

    -
    par2
    +
    par2

    integer; single number or vector of size length(u1); second parameter for the t-Copula; default is par2 = 0, should be an positive integer for the Students's t copula family = 2.

    -
    deriv
    +
    deriv

    Derivative argument
    "par" = second derivative with respect to the first parameter (default)
    "par2" = second derivative with respect to the second parameter (only available for the t-copula)
    "u2" = second derivative with respect to @@ -106,12 +108,12 @@

    Arguments

    and the second argument (only available for the t-copula)

    -
    obj
    +
    obj

    BiCop object containing the family and parameter specification.

    -
    check.pars
    +
    check.pars

    logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

    @@ -119,9 +121,7 @@

    Arguments

    Value

    - - -

    A numeric vector of the second-order conditional bivariate copula +

    A numeric vector of the second-order conditional bivariate copula derivative

    • of the copula family

    • with parameter(s) par, par2

    • with respect to deriv

      • @@ -222,15 +222,15 @@

      Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopHinv.html b/docs/reference/BiCopHinv.html index a684d78..a32266c 100644 --- a/docs/reference/BiCopHinv.html +++ b/docs/reference/BiCopHinv.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -64,13 +64,15 @@

    Inverse Conditional Distribution Function of a Bivariate Copula

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    numeric vectors of equal length with values in \([0,1]\).

    -
    family
    +
    family

    integer; single number or vector of size length(u1); -defines the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 = rotated Clayton copula (90 degrees)
    +defines the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    @@ -94,24 +96,24 @@

    Arguments

    `234` = rotated Tawn type 2 copula (270 degrees)

    -
    par
    +
    par

    numeric; single number or vector of size length(u1); copula parameter.

    -
    par2
    +
    par2

    numeric; single number or vector of size length(u1); second parameter for bivariate copulas with two parameters (t, BB1, BB6, BB7, BB8, Tawn type 1 and type 2; default: par2 = 0). par2 should be an positive integer for the Students's t copula family = 2.

    -
    obj
    +
    obj

    BiCop object containing the family and parameter specification.

    -
    check.pars
    +
    check.pars

    logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

    @@ -119,9 +121,7 @@

    Arguments

    Value

    - - -

    BiCopHinv returns a list with

    +

    BiCopHinv returns a list with

    hinv1

    Numeric vector of the inverse conditional distribution function (inverse h-function) of the copula family with parameter(s) @@ -174,13 +174,6 @@

    Examples

    # inverse h-functions of the Gaussian copula
 cop <- BiCop(1, 0.5)
 hi <- BiCopHinv(0.1, 0.2, cop)
-hi
-#> $hinv1
-#> [1] 0.08539947
-#> 
-#> $hinv2
-#> [1] 0.06292588
-#> 
 # or using the fast versions
 hi1 <- BiCopHinv1(0.1, 0.2, cop)
 hi2 <- BiCopHinv2(0.1, 0.2, cop)
@@ -210,15 +203,15 @@ 
    Examples
    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopIndTest.html b/docs/reference/BiCopIndTest.html index 1d1932c..a3e1538 100644 --- a/docs/reference/BiCopIndTest.html +++ b/docs/reference/BiCopIndTest.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,13 +60,17 @@

    Independence Test for Bivariate Copula Data

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    Data vectors of equal length with values in \([0,1]\).

    Value

    -
    statistic
    + + +
    statistic

    Test statistic of the independence test.

    p.value
    @@ -103,8 +107,7 @@

    Author

    Examples

    - 
    set.seed(123)
-## Example 1: Gaussian copula with large dependence parameter
+    
    ## Example 1: Gaussian copula with large dependence parameter
 cop <- BiCop(1, 0.7)
 dat <- BiCopSim(500, cop)
 
@@ -144,15 +147,15 @@ 
    Examples
    
 
    
 
 
    
-  
    Site built with pkgdown 2.0.9.
    
+  
    Site built with pkgdown 2.1.1.
    - - + + diff --git a/docs/reference/BiCopKDE.html b/docs/reference/BiCopKDE.html index 19c9798..467b0f7 100644 --- a/docs/reference/BiCopKDE.html +++ b/docs/reference/BiCopKDE.html @@ -7,7 +7,7 @@ - +
    @@ -35,14 +35,14 @@
    - +
    @@ -66,17 +66,19 @@

    Kernel estimate of a Bivariate Copula Density

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    numeric vectors of equal length with values in \([0,1]\).

    -
    type
    +
    type

    plot type; either "contour" or "surface" (partial matching is activated) for a contour or perspective/surface plot respectively.

    -
    margins
    +
    margins

    only relevant for types "contour" and "surface"; options are: "unif" for the original copula density, "norm" for the transformed density with standard normal margins, @@ -86,17 +88,17 @@

    Arguments

    (partial matching is activated). Default is "norm" for type = "contour", and "unif" for type = "surface".

    -
    size
    +
    size

    integer; the plot is based on values on a size x size grid; default is 100 for type = "contour", and 25 for type = "surface".

    -
    kde.pars
    +
    kde.pars

    list of arguments passed to kdecopula::kdecop().

    -
    ...
    +
    ...

    optional arguments passed to contour() or lattice::wireframe().

    @@ -152,15 +154,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopKPlot.html b/docs/reference/BiCopKPlot.html index 07661fb..9bd62d3 100644 --- a/docs/reference/BiCopKPlot.html +++ b/docs/reference/BiCopKPlot.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,22 +60,26 @@

    Kendall's Plot for Bivariate Copula Data

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    Data vectors of equal length with values in \([0,1]\).

    -
    PLOT
    +
    PLOT

    Logical; whether the results are plotted. If PLOT = FALSE, the values W.in and Hi.sort are returned (see below; default: PLOT = TRUE).

    -
    ...
    +
    ...

    Additional plot arguments.

    Value

    -
    W.in
    + + +
    W.in

    W-statistics (x-axis).

    Hi.sort

    H-statistics @@ -166,15 +170,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopLambda.html b/docs/reference/BiCopLambda.html index b169f3d..5d4996c 100644 --- a/docs/reference/BiCopLambda.html +++ b/docs/reference/BiCopLambda.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -69,12 +69,14 @@

    Lambda-Function (Plot) for Bivariate Copula Data

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    Data vectors of equal length with values in \([0,1]\) (default: u1 and u2 = NULL).

    -
    family
    +
    family

    An integer defining the bivariate copula family or indicating the empirical lambda-function:
    "emp" = empirical lambda-function (default)
    1 = Gaussian copula; the theoretical lambda-function is simulated @@ -83,33 +85,35 @@

    Arguments

    copula

    -
    par
    +
    par

    Copula parameter; if the empirical lambda-function is chosen, par = NULL or 0 (default).

    -
    par2
    +
    par2

    Second copula parameter for t-, BB1, BB6, BB7 and BB8 copulas (default: par2 = 0).

    -
    PLOT
    +
    PLOT

    Logical; whether the results are plotted. If PLOT = FALSE, the values
    empLambda and/or theoLambda are returned (see below; default: PLOT = TRUE).

    -
    obj
    +
    obj

    BiCop object containing the family and parameter specification.

    -
    ...
    +
    ...

    Additional plot arguments.

    Value

    -
    empLambda
    + + +
    empLambda

    If the empirical lambda-function is chosen and PLOT = FALSE, a vector of the empirical lambda's is returned.

    @@ -170,8 +174,7 @@

    Author

    Examples

    - 
    set.seed(123)
-# simulate from Clayton copula
+    
    # simulate from Clayton copula
 cop <- BiCop(3, tau = 0.5)
 dat <- BiCopSim(1000, cop)
 
@@ -198,15 +201,15 @@ 
    Examples
    
 
    
 
 
    
-  
    Site built with pkgdown 2.0.9.
    
+  
    Site built with pkgdown 2.1.1.
    - - + + diff --git a/docs/reference/BiCopMetaContour.html b/docs/reference/BiCopMetaContour.html index 8787bfa..3a97529 100644 --- a/docs/reference/BiCopMetaContour.html +++ b/docs/reference/BiCopMetaContour.html @@ -5,7 +5,7 @@ - +
    @@ -33,14 +33,14 @@
    - +
    @@ -77,30 +77,32 @@

    Contour Plot of Bivariate Meta Distribution

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    Data vectors of equal length with values in \([0,1]\) (default: u1 and u2 = NULL).

    -
    bw
    +
    bw

    Bandwidth (smoothing factor; default: bw = 1).

    -
    size
    +
    size

    Number of grid points; default: size = 100.

    -
    levels
    +
    levels

    Vector of contour levels. For Gaussian, Student-t or exponential margins the default value (levels = c(0.01, 0.05, 0.1, 0.15, 0.2)) typically is a good choice. For uniform margins we recommend
    levels = c(0.1, 0.3, 0.5, 0.7, 0.9, 1.1, 1.3, 1.5)
    and for Gamma margins
    levels = c(0.005, 0.01, 0.03, 0.05, 0.07, 0.09).

    -
    family
    +
    family

    An integer defining the bivariate copula family or indicating an empirical contour plot:
    "emp" = empirical contour plot -(default; margins can be specified by margins)
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 = rotated Clayton copula (90 degrees)
    +(default; margins can be specified by margins)
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    @@ -124,22 +126,22 @@

    Arguments

    `234` = rotated Tawn type 2 copula (270 degrees)

    -
    par
    +
    par

    Copula parameter; if empirical contour plot, par = NULL or 0 (default).

    -
    par2
    +
    par2

    Second copula parameter for t-, BB1, BB6, BB7, BB8, Tawn type 1 and type 2 copulas (default: par2 = 0).

    -
    PLOT
    +
    PLOT

    Logical; whether the results are plotted. If PLOT = FALSE, the values x, y and z are returned (see below; default: PLOT = TRUE).

    -
    margins
    +
    margins

    Character; margins for the bivariate copula contour plot. Possible margins are:
    "norm" = standard normal margins (default)
    "t" = Student t margins with degrees of freedom as specified by margins.par
    "gamma" = Gamma margins with shape and scale as @@ -147,7 +149,7 @@

    Arguments

    specified by margins.par
    "unif" = uniform margins

    -
    margins.par
    +
    margins.par

    Parameter(s) of the distribution of the margins if necessary (default: margins.par = 0), i.e.,

    • a positive real number for the degrees of freedom of Student t margins (see dt()),

      • @@ -158,23 +160,25 @@

      Arguments

    -
    xylim
    +
    xylim

    A 2-dimensional vector of the x- and y-limits. By default (xylim = NA) standard limits for the selected margins are used.

    -
    obj
    +
    obj

    BiCop object containing the family and parameter specification.

    -
    ...
    +
    ...

    Additional plot arguments.

    Value

    -
    x
    + + +
    x

    A vector of length size with the x-values of the kernel density estimator with Gaussian kernel if the empirical contour plot is chosen and a sequence of values in xylim if the theoretical @@ -260,15 +264,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopName.html b/docs/reference/BiCopName.html index 1f52baf..91a4c75 100644 --- a/docs/reference/BiCopName.html +++ b/docs/reference/BiCopName.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,12 +60,14 @@

    Bivariate Copula Family Names

    Arguments

    -
    family
    + + +
    family

    Bivariate copula family, either its number or its character expression (see table below).

    No.Short nameLong name
    0"I""Independence"
    1"N""Gaussian"
    2"t""t"
    3"C""Clayton"
    4"G""Gumbel"
    5"F""Frank"
    6"J""Joe"
    7"BB1""BB1"
    8"BB6""BB6"
    9"BB7""BB7"
    10"BB8""Frank-Joe"
    13"SC""Survival Clayton"
    14"SG""Survival Gumbel"
    16"SJ""Survival Joe"
    17"SBB1""Survival BB1"
    18"SBB6""Survival BB6"
    19"SBB7""Survival BB7"
    20"SBB8""Survival BB8"
    23"C90""Rotated Clayton 90 degrees"
    24"G90""Rotated Gumbel 90 degrees"
    26"J90""Rotated Joe 90 degrees"
    27"BB1_90""Rotated BB1 90 degrees"
    28"BB6_90""Rotated BB6 90 degrees"
    29"BB7_90""Rotated BB7 90 degrees"
    30"BB8_90""Rotated Frank-Joe 90 degrees"
    33"C270""Rotated Clayton 270 degrees"
    34"G270""Rotated Gumbel 270 degrees"
    36"J270""Rotated Joe 270 degrees"
    37"BB1_270""Rotated BB1 270 degrees"
    38"BB6_270""Rotated BB6 270 degrees"
    39"BB7_270""Rotated BB7 270 degrees"
    40"BB8_270""Rotated Frank-Joe 270 degrees"
    104"Tawn""Tawn type 1"
    114"Tawn180""Rotated Tawn type 1 180 degrees"
    124"Tawn90""Rotated Tawn type 1 90 degrees"
    134"Tawn270""Rotated Tawn type 1 270 degrees"
    204"Tawn2""Tawn type 2"
    214"Tawn2_180""Rotated Tawn type 2 180 degrees"
    224"Tawn2_90""Rotated Tawn type 2 90 degrees"
    234"Tawn2_270""Rotated Tawn type 2 270 degrees"
    -
    short
    +
    short

    Logical; if the number of a bivariate copula family is used and short = TRUE (default), a short version of the corresponding character expression is returned, otherwise the long version.

    @@ -73,9 +75,7 @@

    Arguments

    Value

    - - -

    The transformed bivariate copula family (see table above).

    +

    The transformed bivariate copula family (see table above).

    See also

    @@ -129,15 +129,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopPDF.html b/docs/reference/BiCopPDF.html index b850fc3..82d2cf5 100644 --- a/docs/reference/BiCopPDF.html +++ b/docs/reference/BiCopPDF.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,13 +60,15 @@

    Density of a Bivariate Copula

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    numeric vectors of equal length with values in \([0,1]\).

    -
    family
    +
    family

    integer; single number or vector of size length(u1); -defines the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 = rotated Clayton copula (90 degrees)
    +defines the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    @@ -90,24 +92,24 @@

    Arguments

    `234` = rotated Tawn type 2 copula (270 degrees)

    -
    par
    +
    par

    numeric; single number or vector of size length(u1); copula parameter.

    -
    par2
    +
    par2

    numeric; single number or vector of size length(u1); second parameter for bivariate copulas with two parameters (t, BB1, BB6, BB7, BB8, Tawn type 1 and type 2; default: par2 = 0). par2 should be an positive integer for the Students's t copula family = 2.

    -
    obj
    +
    obj

    BiCop object containing the family and parameter specification.

    -
    check.pars
    +
    check.pars

    logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

    @@ -115,9 +117,7 @@

    Arguments

    Value

    - - -

    A numeric vector of the bivariate copula density

    • of the copula family

      • +

      A numeric vector of the bivariate copula density

      • of the copula family

      • with parameter(s) par, par2

      • evaluated at u1 and u2.

    @@ -138,8 +138,7 @@

    Author

    Examples

    - 
    set.seed(123)
-## simulate from a bivariate Student-t copula
+    
    ## simulate from a bivariate Student-t copula
 cop <- BiCop(family = 2, par = -0.7, par2 = 4)
 simdata <- BiCopSim(100, cop)
 
@@ -213,15 +212,15 @@ 
    Examples
    
 
    
 
 
    
-  
    Site built with pkgdown 2.0.9.
    
+  
    Site built with pkgdown 2.1.1.
    - - + + diff --git a/docs/reference/BiCopPar2Beta.html b/docs/reference/BiCopPar2Beta.html index 27516d9..86164b9 100644 --- a/docs/reference/BiCopPar2Beta.html +++ b/docs/reference/BiCopPar2Beta.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,9 +60,11 @@

    Blomqvist's Beta Value of a Bivariate Copula

    Arguments

    -
    family
    + + +
    family

    integer; single number or vector of size n; defines the -bivariate copula family:
    0 = independence copula
    2 = Student t copula (t-copula)
    1 = Gaussian copula
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 = rotated Clayton copula (90 degrees)
    +bivariate copula family:
    0 = independence copula
    2 = Student t copula (t-copula)
    1 = Gaussian copula
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    @@ -88,23 +90,23 @@

    Arguments

    is not implemented (see BiCopCDF()).

    -
    par
    +
    par

    numeric; single number or vector of size n; copula parameter.

    -
    par2
    +
    par2

    numeric; single number or vector of size n; second parameter for the two parameter BB1, BB6, BB7, BB8, Tawn type 1 and type 2 copulas (default: par2 = 0).

    -
    obj
    +
    obj

    BiCop object containing the family and parameter specification.

    -
    check.pars
    +
    check.pars

    logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

    @@ -112,9 +114,7 @@

    Arguments

    Value

    - - -

    Theoretical value of Blomqvist's beta corresponding to the bivariate +

    Theoretical value of Blomqvist's beta corresponding to the bivariate copula family and parameter(s) par, par2.

    @@ -168,15 +168,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopPar2TailDep.html b/docs/reference/BiCopPar2TailDep.html index 5455c0f..e170f81 100644 --- a/docs/reference/BiCopPar2TailDep.html +++ b/docs/reference/BiCopPar2TailDep.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,9 +60,11 @@

    Tail Dependence Coefficients of a Bivariate Copula

    Arguments

    -
    family
    + + +
    family

    integer; single number or vector of size n; defines the -bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 = rotated Clayton copula (90 degrees)
    +bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    @@ -86,23 +88,23 @@

    Arguments

    `234` = rotated Tawn type 2 copula (270 degrees)

    -
    par
    +
    par

    numeric; single number or vector of size n; copula parameter.

    -
    par2
    +
    par2

    numeric; single number or vector of size n; second parameter for bivariate copulas with two parameters (t, BB1, BB6, BB7, BB8, Tawn type 1 and type 2; default: par2 = 0). par2 should be an positive integer for the Students's t copula family = 2.

    -
    obj
    +
    obj

    BiCop object containing the family and parameter specification.

    -
    check.pars
    +
    check.pars

    logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

    @@ -110,7 +112,9 @@

    Arguments

    Value

    -
    lower
    + + +
    lower

    Lower tail dependence coefficient for the given bivariate copula family and parameter(s) par, par2: $$ \lambda_L = \lim_{u\searrow 0}\frac{C(u,u)}{u} $$

    @@ -199,15 +203,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopPar2Tau.html b/docs/reference/BiCopPar2Tau.html index a80550e..198e262 100644 --- a/docs/reference/BiCopPar2Tau.html +++ b/docs/reference/BiCopPar2Tau.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,9 +60,11 @@

    Kendall's Tau Value of a Bivariate Copula

    Arguments

    -
    family
    + + +
    family

    integer; single number or vector of size m; defines the -bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 = rotated Clayton copula (90 degrees)
    +bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    @@ -86,12 +88,12 @@

    Arguments

    `234` = rotated Tawn type 2 copula (270 degrees)

    -
    par
    +
    par

    numeric; single number or vector of size n; copula parameter.

    -
    par2
    +
    par2

    numeric; single number or vector of size n; second parameter for bivariate copulas with two parameters (t, BB1, BB6, BB7, BB8, Tawn type 1 and type 2; default: par2 = 0). Note that the degrees of @@ -100,12 +102,12 @@

    Arguments

    choice.

    -
    obj
    +
    obj

    BiCop object containing the family and parameter specification.

    -
    check.pars
    +
    check.pars

    logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

    @@ -113,13 +115,9 @@

    Arguments

    Value

    - - -

    Theoretical value of Kendall's tau (vector) corresponding to the -bivariate copula family and parameter vector \((\theta, \delta) =\)

    - - -

    (par, par2).

    No. (family)Kendall's tau (tau)
    1, 2\(\frac{2}{\pi}\arcsin(\theta)\)
    3, 13\(\frac{\theta}{\theta+2}\)
    4, 14\(1-\frac{1}{\theta}\)
    5\(1-\frac{4}{\theta}+4\frac{D_1(\theta)}{\theta}\)
    with \(D_1(\theta)=\int_0^\theta \frac{x/\theta}{\exp(x)-1}dx\) (Debye function)
    6, 16\(1+\frac{4}{\theta^2}\int_0^1 +

    Theoretical value of Kendall's tau (vector) corresponding to the +bivariate copula family and parameter vector \((\theta, \delta) =\) +(par, par2).

    No. (family)Kendall's tau (tau)
    1, 2\(\frac{2}{\pi}\arcsin(\theta)\)
    3, 13\(\frac{\theta}{\theta+2}\)
    4, 14\(1-\frac{1}{\theta}\)
    5\(1-\frac{4}{\theta}+4\frac{D_1(\theta)}{\theta}\)
    with \(D_1(\theta)=\int_0^\theta \frac{x/\theta}{\exp(x)-1}dx\) (Debye function)
    6, 16\(1+\frac{4}{\theta^2}\int_0^1 x\log(x)(1-x)^{2(1-\theta)/\theta}dx\)
    7, 17\(1-\frac{2}{\delta(\theta+2)}\)
    8, 18\(1+4\int_0^1 -\log(-(1-t)^\theta+1) (1-t-(1-t)^{-\theta}+(1-t)^{-\theta}t)/(\delta\theta) dt\)
    9, 19\(1+4\int_0^1 ( (1-(1-t)^{\theta})^{-\delta} - 1) /( -\theta\delta(1-t)^{\theta-1}(1-(1-t)^{\theta})^{-\delta-1} ) dt\)
    10, 20\(1+4\int_0^1 @@ -182,157 +180,6 @@

    Examples

    BiCopPar2Tau(family = c(3,4,6), par = theta) #> [1] 0.4 0.5 0.6 -# \dontshow{ -# Test BiCopPar2Tau (one parametric families) -theta <- BiCopTau2Par(family = 0, tau = c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 0, par = theta) -#> [1] 0 0 0 -theta <- BiCopTau2Par(family = 1, tau = c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 1, par = theta) -#> [1] 0.4 0.5 0.6 -theta <- BiCopTau2Par(family = 3, tau = c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 3, par = theta) -#> [1] 0.4 0.5 0.6 -theta <- BiCopTau2Par(family = 4, tau = c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 4, par = theta) -#> [1] 0.4 0.5 0.6 -theta <- BiCopTau2Par(family = 5, tau = c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 5, par = theta) -#> [1] 0.4 0.5 0.6 -theta <- BiCopTau2Par(family = 6, tau = c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 6, par = theta) -#> [1] 0.4 0.5 0.6 -theta <- BiCopTau2Par(family = 13, tau = c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 13, par = theta) -#> [1] 0.4 0.5 0.6 -theta <- BiCopTau2Par(family = 14, tau = c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 14, par = theta) -#> [1] 0.4 0.5 0.6 -theta <- BiCopTau2Par(family = 16, tau = c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 16, par = theta) -#> [1] 0.4 0.5 0.6 -theta <- BiCopTau2Par(family = 23, tau = -c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 23, par = theta) -#> [1] -0.4 -0.5 -0.6 -theta <- BiCopTau2Par(family = 24, tau = -c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 24, par = theta) -#> [1] -0.4 -0.5 -0.6 -theta <- BiCopTau2Par(family = 26, tau = -c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 26, par = theta) -#> [1] -0.4 -0.5 -0.6 -theta <- BiCopTau2Par(family = 33, tau = -c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 33, par = theta) -#> [1] -0.4 -0.5 -0.6 -theta <- BiCopTau2Par(family = 34, tau = -c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 34, par = theta) -#> [1] -0.4 -0.5 -0.6 -theta <- BiCopTau2Par(family = 36, tau = -c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 36, par = theta) -#> [1] -0.4 -0.5 -0.6 -theta <- BiCopTau2Par(family = 41, tau = c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 41, par = theta) -#> [1] 0.4 0.5 0.6 -theta <- BiCopTau2Par(family = 51, tau = c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 51, par = theta) -#> [1] 0.4 0.5 0.6 -theta <- BiCopTau2Par(family = 61, tau = c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 61, par = theta) -#> [1] 0.4 0.5 0.6 -theta <- BiCopTau2Par(family = 71, tau = c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 71, par = theta) -#> [1] 0.4 0.5 0.6 -theta <- BiCopTau2Par(family = 41, tau = -c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 41, par = theta) -#> [1] -0.4 -0.5 -0.6 -theta <- BiCopTau2Par(family = 51, tau = -c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 51, par = theta) -#> [1] -0.4 -0.5 -0.6 -theta <- BiCopTau2Par(family = 61, tau = -c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 61, par = theta) -#> [1] -0.4 -0.5 -0.6 -theta <- BiCopTau2Par(family = 71, tau = -c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 71, par = theta) -#> [1] -0.4 -0.5 -0.6 - -# Test BiCopPar2Tau (two parametric families) -theta <- BiCopTau2Par(family = 2, tau = c(0.4,0.5,0.6)) -BiCopPar2Tau(family = 2, par = theta) -#> [1] 0.4 0.5 0.6 -theta <- 1:3 -delta <- 1:3 -BiCopPar2Tau(family = 7, par = theta, par2 = delta) -#> [1] 0.3333333 0.7500000 0.8666667 -BiCopPar2Tau(family = 17, par = theta, par2 = delta) -#> [1] 0.3333333 0.7500000 0.8666667 -theta <- -(1:3) -delta <- -(1:3) -BiCopPar2Tau(family = 27, par = theta, par2 = delta) -#> [1] -0.3333333 -0.7500000 -0.8666667 -BiCopPar2Tau(family = 37, par = theta, par2 = delta) -#> [1] -0.3333333 -0.7500000 -0.8666667 -theta <- 2:4 -delta <- 1:3 -BiCopPar2Tau(family = 8, par = theta, par2 = delta) -#> [1] 0.3550658 0.7589812 0.8712351 -BiCopPar2Tau(family = 18, par = theta, par2 = delta) -#> [1] 0.3550658 0.7589812 0.8712351 -theta <- -(2:4) -delta <- -(1:3) -BiCopPar2Tau(family = 28, par = theta, par2 = delta) -#> [1] -0.3550658 -0.7589812 -0.8712351 -BiCopPar2Tau(family = 38, par = theta, par2 = delta) -#> [1] -0.3550658 -0.7589812 -0.8712351 -theta <- 1:3 -delta <- 1:3 -BiCopPar2Tau(family = 9, par = theta, par2 = delta) -#> [1] 0.3333333 0.5833333 0.6848485 -BiCopPar2Tau(family = 19, par = theta, par2 = delta) -#> [1] 0.3333333 0.5833333 0.6848485 -theta <- -(1:3) -delta <- -(1:3) -BiCopPar2Tau(family = 29, par = theta, par2 = delta) -#> [1] -0.3333333 -0.5833333 -0.6848485 -BiCopPar2Tau(family = 39, par = theta, par2 = delta) -#> [1] -0.3333333 -0.5833333 -0.6848485 -theta <- 2:4 -delta <- c(0.1, 0.5, 0.9) -BiCopPar2Tau(family = 10, par = theta, par2 = delta) -#> [1] 0.01200125 0.16649954 0.53531633 -BiCopPar2Tau(family = 20, par = theta, par2 = delta) -#> [1] 0.01200125 0.16649954 0.53531633 -theta <- -(2:4) -delta <- -c(0.1, 0.5, 0.9) -BiCopPar2Tau(family = 30, par = theta, par2 = delta) -#> [1] -0.01200125 -0.16649954 -0.53531633 -BiCopPar2Tau(family = 40, par = theta, par2 = delta) -#> [1] -0.01200125 -0.16649954 -0.53531633 - -theta <- 2:4 -delta <- c(0.1, 0.5, 0.9) -BiCopPar2Tau(family = 104, par = theta, par2 = delta) -#> [1] 0.08268413 0.38629436 0.68897031 -BiCopPar2Tau(family = 114, par = theta, par2 = delta) -#> [1] 0.08268413 0.38629436 0.68897031 -theta <- -(2:4) -delta <- c(0.1, 0.5, 0.9) -BiCopPar2Tau(family = 124, par = theta, par2 = delta) -#> [1] -0.08268413 -0.38629436 -0.68897031 -BiCopPar2Tau(family = 134, par = theta, par2 = delta) -#> [1] -0.08268413 -0.38629436 -0.68897031 - -theta <- 2:4 -delta <- c(0.1, 0.5, 0.9) -BiCopPar2Tau(family = 204, par = theta, par2 = delta) -#> [1] 0.08268413 0.38629436 0.68897031 -BiCopPar2Tau(family = 214, par = theta, par2 = delta) -#> [1] 0.08268413 0.38629436 0.68897031 -theta <- -(2:4) -delta <- c(0.1, 0.5, 0.9) -BiCopPar2Tau(family = 224, par = theta, par2 = delta) -#> [1] -0.08268413 -0.38629436 -0.68897031 -BiCopPar2Tau(family = 234, par = theta, par2 = delta) -#> [1] -0.08268413 -0.38629436 -0.68897031 -# } @@ -348,15 +195,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopSelect.html b/docs/reference/BiCopSelect.html index e5dd7a8..d33c3bb 100644 --- a/docs/reference/BiCopSelect.html +++ b/docs/reference/BiCopSelect.html @@ -5,7 +5,7 @@ - +
    @@ -33,14 +33,14 @@
    - +
    @@ -74,18 +74,20 @@

    Selection and Maximum Likelihood Estimation of Bivariate Copula Families

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    Data vectors of equal length with values in \([0,1]\).

    -
    familyset
    +
    familyset

    Vector of bivariate copula families to select from. The vector has to include at least one bivariate copula family that allows for positive and one that allows for negative dependence. If familyset = NA (default), selection among all possible families is performed. If a vector of negative numbers is provided, selection among all but abs(familyset) families is performed. Coding of bivariate copula -families:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 = rotated Clayton copula (90 degrees)
    +families:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    @@ -109,13 +111,13 @@

    Arguments

    `234` = rotated Tawn type 2 copula (270 degrees)

    -
    selectioncrit
    +
    selectioncrit

    Character indicating the criterion for bivariate copula selection. Possible choices: selectioncrit = "AIC" (default), "BIC", or "logLik".

    -
    indeptest
    +
    indeptest

    Logical; whether a hypothesis test for the independence of u1 and u2 is performed before bivariate copula selection (default: indeptest = FALSE; see BiCopIndTest()). The @@ -123,32 +125,32 @@

    Arguments

    be rejected.

    -
    level
    +
    level

    Numeric; significance level of the independence test (default: level = 0.05).

    -
    weights
    +
    weights

    Numerical; weights for each observation (optional).

    -
    rotations
    +
    rotations

    If TRUE, all rotations of the families in familyset are included (or subtracted).

    -
    se
    +
    se

    Logical; whether standard error(s) of parameter estimates is/are estimated (default: se = FALSE).

    -
    presel
    +
    presel

    Logical; whether to exclude families before fitting based on symmetry properties of the data. Makes the selection about 30% faster (on average), but may yield slightly worse results in few special cases.

    -
    method
    +
    method

    indicates the estimation method: either maximum likelihood estimation (method = "mle"; default) or inversion of Kendall's tau (method = "itau"). For method = "itau" only @@ -159,9 +161,7 @@

    Arguments

    Value

    - - -

    An object of class BiCop(), augmented with the following +

    An object of class BiCop(), augmented with the following entries:

    se, se2

    standard errors for the parameter estimates (if @@ -363,15 +363,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopSim.html b/docs/reference/BiCopSim.html index f6bf7e3..c55c16e 100644 --- a/docs/reference/BiCopSim.html +++ b/docs/reference/BiCopSim.html @@ -3,7 +3,7 @@ - +
    @@ -31,14 +31,14 @@
    - +
    @@ -58,13 +58,15 @@

    Simulation from a Bivariate Copula

    Arguments

    -
    N
    + + +
    N

    Number of bivariate observations simulated.

    -
    family
    +
    family

    integer; single number or vector of size N; defines the -bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 = rotated Clayton copula (90 degrees)
    +bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    @@ -88,24 +90,24 @@

    Arguments

    `234` = rotated Tawn type 2 copula (270 degrees)

    -
    par
    +
    par

    numeric; single number or vector of size N; copula parameter.

    -
    par2
    +
    par2

    numeric; single number or vector of size N; second parameter for bivariate copulas with two parameters (t, BB1, BB6, BB7, BB8, Tawn type 1 and type 2; default: par2 = 0). par2 should be a positive integer for the Students's t copula family = 2.

    -
    obj
    +
    obj

    BiCop object containing the family and parameter specification.

    -
    check.pars
    +
    check.pars

    logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

    @@ -113,9 +115,7 @@

    Arguments

    Value

    - - -

    An N x 2 matrix of data simulated from the bivariate copula +

    An N x 2 matrix of data simulated from the bivariate copula with family and parameter(s) par, par2.

    @@ -156,15 +156,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopTau2Par.html b/docs/reference/BiCopTau2Par.html index 45ea8cc..bf5ac5e 100644 --- a/docs/reference/BiCopTau2Par.html +++ b/docs/reference/BiCopTau2Par.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,12 +60,14 @@

    Parameter of a Bivariate Copula for a given Kendall's Tau Value

    Arguments

    -
    family
    + + +
    family

    integer; single number or vector of size n; defines the bivariate copula family:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (Here only the first parameter can be computed)
    3 = Clayton copula
    4 = -Gumbel copula
    5 = Frank copula
    6 = Joe copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; ``survival Joe'')
    23 +Gumbel copula
    5 = Frank copula
    6 = Joe copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; “survival Joe”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `33` = rotated Clayton copula (270 degrees)
    `34` = rotated Gumbel copula @@ -74,21 +76,19 @@

    Arguments

    cannot be used.

    -
    tau
    +
    tau

    numeric; single number or vector of size n; Kendall's tau value (vector with elements in \([-1,1]\)).

    -
    check.taus
    +
    check.taus

    logical; default is TRUE; if FALSE, checks for family/tau-consistency are omitted (should only be used with care).

    Value

    - - -

    Parameter (vector) corresponding to the bivariate copula family and +

    Parameter (vector) corresponding to the bivariate copula family and the value(s) of Kendall's tau (\(\tau\)).

    + + @@ -323,15 +327,15 @@

    All functions
    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/pairs.copuladata.html b/docs/reference/pairs.copuladata.html index 037347c..adbbb95 100644 --- a/docs/reference/pairs.copuladata.html +++ b/docs/reference/pairs.copuladata.html @@ -5,7 +5,7 @@ - +
    @@ -33,14 +33,14 @@
    - +
    @@ -57,7 +57,7 @@

    Pairs Plot of Copula Data

    - 
    # S3 method for copuladata
+    
    # S3 method for class 'copuladata'
 pairs(
   x,
   labels = names(x),
@@ -76,59 +76,61 @@ 
    Pairs Plot of Copula Data
    
 
     
    
     
    Arguments
    
-    
    x
    
+
+
+
    x
    
 
    copuladata object.
    
 
 
-
    labels
    
+
    labels
    
 
    variable names/labels.
    
 
 
-
    ...
    
+
    ...
    
 
    other graphical parameters (see graphics::par()) or
 options passed to BiCopKDE().
    
 
 
-
    lower.panel
    
+
    lower.panel
    
 
    panel function to be used on the lower diagonal panels
 (if not supplied, a default function is used)
    
 
 
-
    upper.panel
    
+
    upper.panel
    
 
    panel function to be used on the upper diagonal panels
 (if not supplied, a default function is used)
    
 
 
-
    diag.panel
    
+
    diag.panel
    
 
    panel function to be used on the diagonal panels (if not
 supplied, a default function is used)
    
 
 
-
    label.pos
    
+
    label.pos
    
 
    y position of labels in the diagonal panel; default:
 label.pos = 0.85.
    
 
 
-
    cex.labels
    
+
    cex.labels
    
 
    magnification to be used for the labels of the diagonal
 panel; default: cex.labels = 1.
    
 
 
-
    gap
    
+
    gap
    
 
    distance between subplots, in margin lines; default: gap = 0.
    
 
 
-
    method
    
+
    method
    
 
    a character string indicating which correlation coefficients
 are computed. One of "pearson", "kendall" (default), or
 "spearman"
    
 
 
-
    ccols
    
+
    ccols
    
 
    color to be used for the contour plots; default: ccols = terrain.colors(30).
    
 
 
-
    margins
    
+
    margins
    
 
    character; margins for the contour plots. Options are:
    "unif" for the original copula density,
 "norm" for the transformed density with standard normal margins,
 "exp" with standard exponential margins, and  "flexp" with
@@ -157,7 +159,6 @@ 
    Author
    
     
    Examples
    
     
    
 data(daxreturns)
-daxreturns <- daxreturns[1:50, ]
 data <- as.copuladata(daxreturns)
 sel <- c(4,5,14,15)
 
@@ -222,15 +223,15 @@ 
    Examples
    
 
    
 
 
    
-  
    Site built with pkgdown 2.0.9.
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
       
    
 
-  
 
 
-  
+
+
 
   
 
diff --git a/docs/reference/plot.BiCop.html b/docs/reference/plot.BiCop.html
index 1de3573..1ecfc5a 100644
--- a/docs/reference/plot.BiCop.html
+++ b/docs/reference/plot.BiCop.html
@@ -7,7 +7,7 @@
 
 
 
-    
+
 
     
    
       
    
 
@@ -35,14 +35,14 @@
    - +
    @@ -61,26 +61,28 @@

    Plotting tools for BiCop objects

    - 
    # S3 method for BiCop
+    
    # S3 method for class 'BiCop'
 plot(x, type = "surface", margins, size, ...)
 
-# S3 method for BiCop
+# S3 method for class 'BiCop'
 contour(x, margins = "norm", size = 100L, ...)

    Arguments

    -
    x
    + + +
    x

    BiCop object.

    -
    type
    +
    type

    plot type; either "surface", "contour", or "lambda" (partial matching is activated); the latter is only implemented for a few families (c.f., BiCopLambda()).

    -
    margins
    +
    margins

    only relevant for types "contour" and "surface"; options are: "unif" for the original copula density, "norm" for the transformed density with standard normal margins, @@ -88,13 +90,13 @@

    Arguments

    flipped exponential margins. Default is "norm" for type = "contour", and "unif" for type = "surface".

    -
    size
    +
    size

    integer; only relevant for types "contour" and "surface"; the plot is based on values on a \(size x size\) grid; default is 100 for type = "contour", and 25 for type = "surface".

    -
    ...
    +
    ...

    optional arguments passed to contour() or lattice::wireframe().

    @@ -136,15 +138,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/plot.RVineMatrix.html b/docs/reference/plot.RVineMatrix.html index 93bc7df..e26073f 100644 --- a/docs/reference/plot.RVineMatrix.html +++ b/docs/reference/plot.RVineMatrix.html @@ -7,7 +7,7 @@ - +
    @@ -35,14 +35,14 @@
    - +
    @@ -61,10 +61,10 @@

    Plotting RVineMatrix objects.

    - 
    # S3 method for RVineMatrix
+    
    # S3 method for class 'RVineMatrix'
 contour(x, tree = "ALL", xylim = NULL, cex.nums = 1, data = NULL, ...)
 
-# S3 method for RVineMatrix
+# S3 method for class 'RVineMatrix'
 plot(
   x,
   tree = "ALL",
@@ -78,41 +78,43 @@ 
    Plotting RVineMatrix objects.
    
 
     
    
     
    Arguments
    
-    
    x
    
+
+
+
    x
    
 
    RVineMatrix object.
    
 
 
-
    tree
    
+
    tree
    
 
    "ALL" or integer vector; specifies which trees are
 plotted.
    
 
 
-
    xylim
    
+
    xylim
    
 
    numeric vector of length 2; sets xlim and ylim
 for the contours
    
 
 
-
    cex.nums
    
+
    cex.nums
    
 
    numeric; expansion factor for font of the numbers.
    
 
 
-
    data
    
+
    data
    
 
    a data matrix for creating kernel density contours of each pair.
    
 
 
-
    ...
    
+
    ...
    
 
    Arguments passed to
 network::plot.network() or
 plot.BiCop() respectively.
    
 
 
-
    type
    
+
    type
    
 
    integer; specifies how to make use of variable names: 
    0 = variable names are ignored, 
    1 = variable names are
 used to annotate vertices, 
    2 = uses numbers in plot and adds a
 legend for variable names.
    
 
 
-
    edge.labels
    
+
    edge.labels
    
 
    character; either a vector of edge labels or one of the
 following: 
    "family" = pair-copula family abbreviation (see
 BiCopName()), 
    "par" =
@@ -121,12 +123,12 @@ 
    Arguments
    
 parameters 
    "family-tau" = pair-copula family and Kendall's tau.
    
 
 
-
    legend.pos
    
+
    legend.pos
    
 
    the x argument for
 graphics::legend().
    
 
 
-
    interactive
    
+
    interactive
    
 
    logical; if TRUE, the user is asked to adjust the
 positioning of vertices with his mouse.
    
 
@@ -160,7 +162,7 @@ 
    Examples
    
 RVM  <- RVineMatrix(strucmat, fammat, parmat, par2mat)
 
 # plot trees
-if (FALSE) plot(RVM)
+if (FALSE) plot(RVM) # \dontrun{}
 
 # show contour plots
 contour(RVM)
@@ -180,15 +182,15 @@ 
    Examples
    
 
    
 
 
    
-  
    Site built with pkgdown 2.0.9.
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
       
    
 
-  
 
 
-  
+
+
 
   
 
diff --git a/docs/reference/pobs.html b/docs/reference/pobs.html
index ec98a00..687d5d9 100644
--- a/docs/reference/pobs.html
+++ b/docs/reference/pobs.html
@@ -3,7 +3,7 @@
 
 
 
-    
+
 
     
    
       
    
 
@@ -31,14 +31,14 @@
    - +
    @@ -63,25 +63,25 @@

    Pseudo-Observations

    Arguments

    -
    x
    + + +
    x

    \(n\times d\)-matrix of random variates to be converted to pseudo-observations.

    -
    na.last, ties.method
    +
    na.last, ties.method

    are passed to rank(); see there.

    -
    lower.tail
    +
    lower.tail

    logical() which, if FALSE, returns the pseudo-observations when applying the empirical marginal survival functions.

    Value

    - - -

    matrix of the same dimensions as x containing the +

    matrix of the same dimensions as x containing the pseudo-observations.

    @@ -131,7 +131,7 @@

    Examples

    #> U #> else 1 - U #> } -#> <bytecode: 0x55c5c2eb2a98> +#> <bytecode: 0x5633151cd8d0> #> <environment: namespace:VineCopula> ## simulate data from a multivariate normal distribution @@ -164,15 +164,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/sitemap.xml b/docs/sitemap.xml index 4b3e3ce..76a9f32 100644 --- a/docs/sitemap.xml +++ b/docs/sitemap.xml @@ -1,279 +1,75 @@ - - - - /404.html - - - /authors.html - - - /index.html - - - /news/index.html - - - /reference/BB1Copula-class.html - - - /reference/BB1Copula.html - - - /reference/BB6Copula-class.html - - - /reference/BB6Copula.html - - - /reference/BB7Copula-class.html - - - /reference/BB7Copula.html - - - /reference/BB8Copula-class.html - - - /reference/BB8Copula.html - - - /reference/BetaMatrix.html - - - /reference/BiCop.html - - - /reference/BiCopCDF.html - - - /reference/BiCopCheck.html - - - /reference/BiCopChiPlot.html - - - /reference/BiCopCompare.html - - - /reference/BiCopCondSim.html - - - /reference/BiCopDeriv.html - - - /reference/BiCopDeriv2.html - - - /reference/BiCopEst.html - - - /reference/BiCopEstList.html - - - /reference/BiCopGofTest.html - - - /reference/BiCopHfunc.html - - - /reference/BiCopHfuncDeriv.html - - - /reference/BiCopHfuncDeriv2.html - - - /reference/BiCopHinv.html - - - /reference/BiCopIndTest.html - - - /reference/BiCopKDE.html - - - /reference/BiCopKPlot.html - - - /reference/BiCopLambda.html - - - /reference/BiCopMetaContour.html - - - /reference/BiCopName.html - - - /reference/BiCopPDF.html - - - /reference/BiCopPar2Beta.html - - - /reference/BiCopPar2TailDep.html - - - /reference/BiCopPar2Tau.html - - - /reference/BiCopSelect.html - - - /reference/BiCopSim.html - - - /reference/BiCopTau2Par.html - - - /reference/BiCopVuongClarke.html - - - /reference/C2RVine.html - - - /reference/D2RVine.html - - - /reference/EmpCDF.html - - - /reference/RVineAIC.html - - - /reference/RVineClarkeTest.html - - - /reference/RVineCopSelect.html - - - /reference/RVineCor2pcor.html - - - /reference/RVineGofTest.html - - - /reference/RVineGrad.html - - - /reference/RVineHessian.html - - - /reference/RVineLogLik.html - - - /reference/RVineMLE.html - - - /reference/RVineMatrix.html - - - /reference/RVineMatrixCheck.html - - - /reference/RVineMatrixNormalize.html - - - /reference/RVineMatrixSample.html - - - /reference/RVinePDF.html - - - /reference/RVinePIT.html - - - /reference/RVinePar2Beta.html - - - /reference/RVinePar2Tau.html - - - /reference/RVineSeqEst.html - - - /reference/RVineSim.html - - - /reference/RVineStdError.html - - - /reference/RVineStructureSelect.html - - - /reference/RVineTreePlot.html - - - /reference/RVineVuongTest.html - - - /reference/TauMatrix.html - - - /reference/VC2copula-deprecated.html - - - /reference/VineCopula-package.html - - - /reference/as.copuladata.html - - - /reference/copulaFromFamilyIndex.html - - - /reference/daxreturns.html - - - /reference/ddCopula.html - - - /reference/index.html - - - /reference/joeBiCopula-class.html - - - /reference/joeBiCopula.html - - - /reference/pairs.copuladata.html - - - /reference/plot.BiCop.html - - - /reference/plot.RVineMatrix.html - - - /reference/pobs.html - - - /reference/surClaytonCopula-class.html - - - /reference/surClaytonCopula.html - - - /reference/surGumbelCopula-class.html - - - /reference/surGumbelCopula.html - - - /reference/tawnT1Copula-class.html - - - /reference/tawnT1Copula.html - - - /reference/tawnT2Copula-class.html - - - /reference/tawnT2Copula.html - - - /reference/vineCopula-class.html - - - /reference/vineCopula.html - + +/404.html +/authors.html +/index.html +/news/index.html +/reference/BetaMatrix.html +/reference/BiCop.html +/reference/BiCopCDF.html +/reference/BiCopCheck.html +/reference/BiCopChiPlot.html +/reference/BiCopCompare.html +/reference/BiCopCondSim.html +/reference/BiCopDeriv.html +/reference/BiCopDeriv2.html +/reference/BiCopEst.html +/reference/BiCopEstList.html +/reference/BiCopGofTest.html +/reference/BiCopHfunc.html +/reference/BiCopHfuncDeriv.html +/reference/BiCopHfuncDeriv2.html +/reference/BiCopHinv.html +/reference/BiCopIndTest.html +/reference/BiCopKDE.html +/reference/BiCopKPlot.html +/reference/BiCopLambda.html +/reference/BiCopMetaContour.html +/reference/BiCopName.html +/reference/BiCopPDF.html +/reference/BiCopPar2Beta.html +/reference/BiCopPar2TailDep.html +/reference/BiCopPar2Tau.html +/reference/BiCopSelect.html +/reference/BiCopSim.html +/reference/BiCopTau2Par.html +/reference/BiCopVuongClarke.html +/reference/C2RVine.html +/reference/D2RVine.html +/reference/EmpCDF.html +/reference/RVineAIC.html +/reference/RVineCDF.html +/reference/RVineClarkeTest.html +/reference/RVineCopSelect.html +/reference/RVineCor2pcor.html +/reference/RVineGofTest.html +/reference/RVineGrad.html +/reference/RVineHessian.html +/reference/RVineLogLik.html +/reference/RVineMLE.html +/reference/RVineMatrix.html +/reference/RVineMatrixCheck.html +/reference/RVineMatrixNormalize.html +/reference/RVineMatrixSample.html +/reference/RVinePDF.html +/reference/RVinePIT.html +/reference/RVinePar2Beta.html +/reference/RVinePar2Tau.html +/reference/RVineSeqEst.html +/reference/RVineSim.html +/reference/RVineStdError.html +/reference/RVineStructureSelect.html +/reference/RVineTreePlot.html +/reference/RVineVuongTest.html +/reference/TauMatrix.html +/reference/VC2copula-deprecated.html +/reference/VineCopula-package.html +/reference/as.copuladata.html +/reference/daxreturns.html +/reference/ddCopula.html +/reference/index.html +/reference/pairs.copuladata.html +/reference/plot.BiCop.html +/reference/plot.RVineMatrix.html +/reference/pobs.html +

    No. (family)Parameter (par)
    1, 2\(\sin(\tau \frac{\pi}{2})\)
    3, 13\(2\frac{\tau}{1-\tau}\)
    4, 14\(\frac{1}{1-\tau}\)
    5no closed form expression (numerical inversion)
    6, 16no closed form @@ -141,57 +141,6 @@

    Examples

    BiCopPar2Tau(family = c(3,4,6), par = theta) #> [1] 0.4 0.5 0.6 -# \dontshow{ -# Test BiCopTau2Par -BiCopTau2Par(family = 0, tau = c(0.4,0.5,0.6)) -#> [1] 0 0 0 -BiCopTau2Par(family = 1, tau = c(0.4,0.5,0.6)) -#> [1] 0.5877853 0.7071068 0.8090170 -BiCopTau2Par(family = 2, tau = c(0.4,0.5,0.6)) -#> [1] 0.5877853 0.7071068 0.8090170 -BiCopTau2Par(family = 3, tau = c(0.4,0.5,0.6)) -#> [1] 1.333333 2.000000 3.000000 -BiCopTau2Par(family = 4, tau = c(0.4,0.5,0.6)) -#> [1] 1.666667 2.000000 2.500000 -BiCopTau2Par(family = 5, tau = c(0.4,0.5,0.6)) -#> [1] 4.168941 5.747564 7.940414 -BiCopTau2Par(family = 6, tau = c(0.4,0.5,0.6)) -#> [1] 2.219070 2.856257 3.826659 -BiCopTau2Par(family = 13, tau = c(0.4,0.5,0.6)) -#> [1] 1.333333 2.000000 3.000000 -BiCopTau2Par(family = 14, tau = c(0.4,0.5,0.6)) -#> [1] 1.666667 2.000000 2.500000 -BiCopTau2Par(family = 16, tau = c(0.4,0.5,0.6)) -#> [1] 2.219070 2.856257 3.826659 -BiCopTau2Par(family = 23, tau = -c(0.4,0.5,0.6)) -#> [1] -1.333333 -2.000000 -3.000000 -BiCopTau2Par(family = 24, tau = -c(0.4,0.5,0.6)) -#> [1] -1.666667 -2.000000 -2.500000 -BiCopTau2Par(family = 26, tau = -c(0.4,0.5,0.6)) -#> [1] -2.219070 -2.856257 -3.826659 -BiCopTau2Par(family = 33, tau = -c(0.4,0.5,0.6)) -#> [1] -1.333333 -2.000000 -3.000000 -BiCopTau2Par(family = 34, tau = -c(0.4,0.5,0.6)) -#> [1] -1.666667 -2.000000 -2.500000 -BiCopTau2Par(family = 36, tau = -c(0.4,0.5,0.6)) -#> [1] -2.219070 -2.856257 -3.826659 -BiCopTau2Par(family = 41, tau = c(0.4,0.5,0.6)) -#> [1] 3.278015 4.836848 7.703827 -BiCopTau2Par(family = 51, tau = c(0.4,0.5,0.6)) -#> [1] 3.278015 4.836848 7.703827 -BiCopTau2Par(family = 61, tau = c(0.4,0.5,0.6)) -#> [1] -0.3583378 -0.2699585 -0.1968076 -BiCopTau2Par(family = 71, tau = c(0.4,0.5,0.6)) -#> [1] -0.3583378 -0.2699585 -0.1968076 -BiCopTau2Par(family = 41, tau = -c(0.4,0.5,0.6)) -#> [1] 0.3583378 0.2699585 0.1968076 -BiCopTau2Par(family = 51, tau = -c(0.4,0.5,0.6)) -#> [1] 0.3583378 0.2699585 0.1968076 -BiCopTau2Par(family = 61, tau = -c(0.4,0.5,0.6)) -#> [1] -3.278015 -4.836848 -7.703827 -BiCopTau2Par(family = 71, tau = -c(0.4,0.5,0.6)) -#> [1] -3.278015 -4.836848 -7.703827 -# } @@ -207,15 +156,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/BiCopVuongClarke.html b/docs/reference/BiCopVuongClarke.html index b431bba..3650cf8 100644 --- a/docs/reference/BiCopVuongClarke.html +++ b/docs/reference/BiCopVuongClarke.html @@ -2,12 +2,12 @@ Scoring Goodness-of-Fit Test based on Vuong And Clarke Tests for Bivariate Copula Data — BiCopVuongClarke • VineCopula - +
    @@ -35,14 +35,14 @@
    - +
    @@ -56,8 +56,8 @@

    Scoring Goodness-of-Fit Test based on Vuong And Clarke Tests for Bivariate C

    Based on the Vuong and Clarke tests this function computes a goodness-of-fit score for each bivariate copula family under consideration. For each possible pair of copula families the Vuong and the Clarke tests decides -which of the two families fits the given data best and assigns a score---pro -or contra a copula family---according to this decision.

    +which of the two families fits the given data best and assigns a score—pro +or contra a copula family—according to this decision.

    @@ -73,15 +73,17 @@

    Scoring Goodness-of-Fit Test based on Vuong And Clarke Tests for Bivariate C

    Arguments

    -
    u1, u2
    + + +
    u1, u2

    Data vectors of equal length with values in \([0,1]\).

    -
    familyset
    +
    familyset

    An integer vector of bivariate copula families under consideration, i.e., which are compared in the goodness-of-fit test. If familyset = NA (default), all possible families are compared. -Possible families are:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 = rotated Clayton copula (90 degrees)
    +Possible families are:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    @@ -105,27 +107,25 @@

    Arguments

    `234` = rotated Tawn type 2 copula (270 degrees)

    -
    correction
    +
    correction

    Correction for the number of parameters. Possible choices: correction = FALSE (no correction; default), "Akaike" and "Schwarz".

    -
    level
    +
    level

    Numerical; significance level of the tests (default: level = 0.05).

    -
    rotations
    +
    rotations

    If TRUE, all rotations of the families in familyset are included (or subtracted).

    Value

    - - -

    A matrix with Vuong test scores in the first and Clarke test scores +

    A matrix with Vuong test scores in the first and Clarke test scores in the second row. Column names correspond to bivariate copula families (see above).

    @@ -186,10 +186,8 @@

    Author

    Examples

    - 
    set.seed(123)
-# simulate from a t-copula
+    
    # simulate from a t-copula
 dat <- BiCopSim(500, 2, 0.7, 5)
-dat <- dat[1:100, ]
 
 # apply the test for families 1-6
 BiCopVuongClarke(dat[,1], dat[,2], familyset = 1:6)
@@ -211,15 +209,15 @@ 
    Examples
    
 
    
 
 
    
-  
    Site built with pkgdown 2.0.9.
    
+  
    Site built with pkgdown 2.1.1.
    - - + + diff --git a/docs/reference/C2RVine.html b/docs/reference/C2RVine.html index 6927d7f..c5ad0e9 100644 --- a/docs/reference/C2RVine.html +++ b/docs/reference/C2RVine.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,18 +60,20 @@

    Transform C-Vine to R-Vine Structure

    Arguments

    -
    order
    + + +
    order

    A d-dimensional vector specifying the order of the root nodes in the C-vine.

    -
    family
    +
    family

    A d*(d-1)/2 vector of pair-copula families with values
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 -degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 -degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 +degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 +degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    `28` = rotated BB6 copula (90 @@ -89,11 +91,11 @@

    Arguments

    `234` = rotated Tawn type 2 copula (270 degrees)

    -
    par
    +
    par

    A d*(d-1)/2 vector of pair-copula parameters.

    -
    par2
    +
    par2

    A d*(d-1)/2 vector of second pair-copula parameters (optional; default:
    par2 = rep(0,length(family))), necessary for the t-, BB1, BB6, BB7, BB8, Tawn type 1 and type 2 copulas.

    @@ -101,9 +103,7 @@

    Arguments

    Value

    - - -

    An RVineMatrix() object.

    +

    An RVineMatrix() object.

    See also

    @@ -140,15 +140,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/D2RVine.html b/docs/reference/D2RVine.html index cdcd7fd..ddb16ab 100644 --- a/docs/reference/D2RVine.html +++ b/docs/reference/D2RVine.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,18 +60,20 @@

    Transform D-Vine to R-Vine Structure

    Arguments

    -
    order
    + + +
    order

    A d-dimensional vector specifying the order of the nodes in the D-vine.

    -
    family
    +
    family

    A d*(d-1)/2 vector of pair-copula families with values
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 -degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 -degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 +degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 +degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    `28` = rotated BB6 copula (90 @@ -89,11 +91,11 @@

    Arguments

    `234` = rotated Tawn type 2 copula (270 degrees)

    -
    par
    +
    par

    A d*(d-1)/2 vector of pair-copula parameters.

    -
    par2
    +
    par2

    A d*(d-1)/2 vector of second pair-copula parameters (optional; default:
    par2 = rep(0,length(family))), necessary for the t-, BB1, BB6, BB7, BB8, Tawn type 1 and type 2 copulas.

    @@ -101,9 +103,7 @@

    Arguments

    Value

    - - -

    An RVineMatrix() object.

    +

    An RVineMatrix() object.

    See also

    @@ -140,15 +140,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/EmpCDF.html b/docs/reference/EmpCDF.html index 5e64c48..7dbab4c 100644 --- a/docs/reference/EmpCDF.html +++ b/docs/reference/EmpCDF.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,15 +60,15 @@

    Corrected Empirical CDF

    Arguments

    -
    x
    + + +
    x

    numeric vector of observations

    Value

    - - -

    A function with signature function(x) that returns \(F_n(x)\).

    +

    A function with signature function(x) that returns \(F_n(x)\).

    Details

    @@ -103,15 +103,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVineAIC.html b/docs/reference/RVineAIC.html index 6a3ea93..605462d 100644 --- a/docs/reference/RVineAIC.html +++ b/docs/reference/RVineAIC.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -62,28 +62,32 @@

    AIC and BIC of an R-Vine Copula Model

    Arguments

    -
    data
    + + +
    data

    An N x d data matrix (with uniform margins).

    -
    RVM
    +
    RVM

    An RVineMatrix() object including the structure and the pair-copula families and parameters.

    -
    par
    +
    par

    A d x d matrix with the pair-copula parameters (optional; default: par = RVM$par).

    -
    par2
    +
    par2

    A d x d matrix with the second parameters of pair-copula families with two parameters (optional; default: par2 = RVM$par2).

    Value

    -
    AIC, BIC
    + + +
    AIC, BIC

    The computed AIC or BIC value, respectively.

    pair.AIC, pair.BIC
    @@ -202,15 +206,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVineCDF.html b/docs/reference/RVineCDF.html new file mode 100644 index 0000000..5d15b42 --- /dev/null +++ b/docs/reference/RVineCDF.html @@ -0,0 +1,172 @@ + +CDF of an R-Vine Copula Model — RVineCDF • VineCopula + + +
    +
    + + + +
    +
    +
    +

    CDF of an R-Vine Copula Model

    + Source: R/RVineLogLik.R + +
    + +
    +

    This function calculates the cumulative distribution +function of a d-dimensional R-vine copula.

    +
    + +
    + 
    RVineCDF(data, RVM, N = 1000)
    +
    + +
    +

    Arguments

    + + +
    data
    +

    An N x d data matrix that specifies where +the CDF shall be evaluated.

    + + +
    RVM
    +

    An RVineMatrix() object including the +structure and the pair-copula families and parameters.

    + + +
    N
    +

    Number of points to simulate for the Monte +Carlo integration (default: n = 1000).

    + +
    +
    +

    Value

    +

    A vector of length N with the CDF values.

    +
    +
    +

    Details

    +

    The cumulative distribution function of a \(d\)-dimensional R-vine copula +cannot be expressed in closed form. +However, it can be calculated by numerical integration. The function uses +the RVineSim() function to +simulate a grid of points and then computes the CDF via Monte Carlo.

    +
    + +
    +

    Author

    +

    Thibault Vatter

    +
    + +
    +

    Examples

    + 
    # define 5-dimensional R-vine tree structure matrix
+Matrix <- c(
+  5, 2, 3, 1, 4,
+  0, 2, 3, 4, 1,
+  0, 0, 3, 4, 1,
+  0, 0, 0, 4, 1,
+  0, 0, 0, 0, 1
+)
+Matrix <- matrix(Matrix, 5, 5)
+
+# define R-vine pair-copula family matrix
+family <- c(
+  0, 1, 3, 4, 4,
+  0, 0, 3, 4, 1,
+  0, 0, 0, 4, 1,
+  0, 0, 0, 0, 3,
+  0, 0, 0, 0, 0
+)
+family <- matrix(family, 5, 5)
+
+# define R-vine pair-copula parameter matrix
+par <- c(
+  0, 0.2, 0.9, 1.5, 3.9,
+  0, 0, 1.1, 1.6, 0.9,
+  0, 0, 0, 1.9, 0.5,
+  0, 0, 0, 0, 4.8,
+  0, 0, 0, 0, 0
+)
+par <- matrix(par, 5, 5)
+
+# define second R-vine pair-copula parameter matrix
+par2 <- matrix(0, 5, 5)
+
+# define RVineMatrix object
+RVM <- RVineMatrix(
+  Matrix = Matrix, family = family,
+  par = par, par2 = par2,
+  names = c("V1", "V2", "V3", "V4", "V5")
+)
+
+# compute the CDF at (0.1, 0.2, 0.3, 0.4, 0.5)
+RVineCDF(c(0.1, 0.2, 0.3, 0.4, 0.5), RVM)
+#> [1] 0.064
+
+
    +
    +
    + +
    + + +
    +

    Developed by Thomas Nagler, Ulf Schepsmeier, Jakob Stoeber, Eike Christian Brechmann, Benedikt Graeler, Tobias Erhardt.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/RVineClarkeTest.html b/docs/reference/RVineClarkeTest.html index 3f6cc11..d96ea0e 100644 --- a/docs/reference/RVineClarkeTest.html +++ b/docs/reference/RVineClarkeTest.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,17 +60,21 @@

    Clarke Test Comparing Two R-Vine Copula Models

    Arguments

    -
    data
    + + +
    data

    An N x d data matrix (with uniform margins).

    -
    RVM1, RVM2
    +
    RVM1, RVM2

    RVineMatrix() objects of models 1 and 2.

    Value

    -
    statistic, statistic.Akaike, statistic.Schwarz
    + + +
    statistic, statistic.Akaike, statistic.Schwarz

    Test statistics without correction, with Akaike correction and with Schwarz correction.

    @@ -128,7 +132,6 @@

    Examples

    # load data set data(daxreturns) -daxreturns <- daxreturns[1:200, ] # select the R-vine structure, families and parameters RVM <- RVineStructureSelect(daxreturns[,1:5], c(1:6)) @@ -203,15 +206,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVineCopSelect.html b/docs/reference/RVineCopSelect.html index b9ed062..6277d21 100644 --- a/docs/reference/RVineCopSelect.html +++ b/docs/reference/RVineCopSelect.html @@ -5,7 +5,7 @@ - +
    @@ -33,14 +33,14 @@
    - +
    @@ -76,11 +76,13 @@

    Sequential Pair-Copula Selection and Estimation for R-Vine Copula Models

    Arguments

    -
    data
    + + +
    data

    N x d data matrix (with uniform margins).

    -
    familyset
    +
    familyset

    integer vector of pair-copula families to select from. The vector has to include at least one pair-copula family that allows for positive and one that allows for negative @@ -91,18 +93,18 @@

    Arguments

    pair copula families is the same as in BiCop().

    -
    Matrix
    +
    Matrix

    lower or upper triangular d x d matrix that defines the R-vine tree structure.

    -
    selectioncrit
    +
    selectioncrit

    Character indicating the criterion for pair-copula selection. Possible choices: selectioncrit = "AIC" (default), "BIC", or "logLik" (see BiCopSelect()).

    -
    indeptest
    +
    indeptest

    Logical; whether a hypothesis test for the independence of u1 and u2 is performed before bivariate copula selection (default: indeptest = FALSE; see BiCopIndTest()). The @@ -110,35 +112,35 @@

    Arguments

    hypothesis of independence cannot be rejected.

    -
    level
    +
    level

    numeric; significance level of the independence test (default: level = 0.05).

    -
    trunclevel
    +
    trunclevel

    integer; level of truncation.

    -
    weights
    +
    weights

    Numerical; weights for each observation (optional).

    -
    rotations
    +
    rotations

    logical; if TRUE, all rotations of the families in familyset are included.

    -
    se
    +
    se

    Logical; whether standard errors are estimated (default: se = FALSE).

    -
    presel
    +
    presel

    Logical; whether to exclude families before fitting based on symmetry properties of the data. Makes the selection about 30\ (on average), but may yield slightly worse results in few special cases.

    -
    method
    +
    method

    indicates the estimation method: either maximum likelihood estimation (method = "mle"; default) or inversion of Kendall's tau (method = "itau"). For method = "itau" only @@ -147,7 +149,7 @@

    Arguments

    interval (2, 10].

    -
    cores
    +
    cores

    integer; if cores > 1, estimation will be parallelized within each tree (using parallel::parLapply()). Note that parallelization causes substantial overhead and may be slower than @@ -157,9 +159,7 @@

    Arguments

    Value

    - - -

    An RVineMatrix() object with the selected families +

    An RVineMatrix() object with the selected families (RVM$family) as well as sequentially estimated parameters stored in RVM$par and RVM$par2. The object is augmented by the following information about the fit:

    @@ -305,7 +305,7 @@

    Examples

    #> 1 <-> V1, 2 <-> V2, 3 <-> V3, 4 <-> V4, 5 <-> V5 ## inspect the fitted model using plots -if (FALSE) plot(RVM1) # tree structure +if (FALSE) plot(RVM1) # tree structure # \dontrun{} contour(RVM1) # contour plots of all pair-copulas @@ -324,15 +324,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVineCor2pcor.html b/docs/reference/RVineCor2pcor.html index b59b6c0..caae547 100644 --- a/docs/reference/RVineCor2pcor.html +++ b/docs/reference/RVineCor2pcor.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -62,19 +62,23 @@

    (Partial) Correlations for R-Vine Copula Models

    Arguments

    -
    RVM
    + + +
    RVM

    RVineMatrix() defining only the R-vine structure for Cor2pcor and providing as well the partial correlations for Pcor2cor.

    -
    corMat
    +
    corMat

    correlation matrix

    Value

    -
    RVM
    + + +
    RVM

    RVineMatrix with transformed partial correlations (for Cor2pcor)

    cor
    @@ -138,15 +142,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVineGofTest.html b/docs/reference/RVineGofTest.html index 3ca7ef8..aa6e345 100644 --- a/docs/reference/RVineGofTest.html +++ b/docs/reference/RVineGofTest.html @@ -5,7 +5,7 @@ - +
    @@ -33,14 +33,14 @@
    - +
    @@ -69,16 +69,18 @@

    Goodness-of-Fit Tests for R-Vine Copula Models

    Arguments

    -
    data
    + + +
    data

    An N x d data matrix (with uniform margins).

    -
    RVM
    +
    RVM

    RVineMatrix() objects of the R-vine model under the null hypothesis.
    Only the following copula families are allowed in RVM$family due to restrictions in RVineGrad() and -RVineHessian()
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; ``survival Joe'')
    23 = rotated Clayton copula (90 degrees)
    +RVineHessian()
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; “survival Joe”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `33` = rotated Clayton copula (270 degrees)
    @@ -86,7 +88,7 @@

    Arguments

    `36` = rotated Joe copula (270 degrees)

    -
    method
    +
    method

    A string indicating the goodness-of-fit method:
    "White" = goodness-of-fit test based on White's information matrix equality (default)
    "IR" = goodness-of-fit test based on the information ratio
    "Breymann" = goodness-of-fit test based on the @@ -101,7 +103,7 @@

    Arguments

    2009)

    -
    statistic
    +
    statistic

    A string indicating the goodness-of-fit test statistic type:
    "CvM" = Cramer-von Mises test statistic (univariate for "Breymann", "Berg" and "Berg2", multivariate for @@ -111,23 +113,21 @@

    Arguments

    "Breymann", "Berg" and "Berg2")

    -
    B
    +
    B

    an integer for the number of bootstrap steps (default B = 200)
    For B = 0 the asymptotic p-value is returned if available, otherwise only the test statistic is returned.
    WARNING: If B is chosen too large, computations will take very long.

    -
    alpha
    +
    alpha

    an integer of the set 2,4,6,... for the "Berg2" goodness-of-fit test (default alpha = 2)

    Value

    - - -

    For method = "White":

    +

    For method = "White":

    White

    test statistic

    @@ -145,10 +145,8 @@

    Value

    Schepsmeier (2013). Be aware, that the test statistics than have to be adjusted with the empirical variance.

    -

    For method = "Breymann", method = "Berg"

    - - -

    and method = "Berg2":

    +

    For method = "Breymann", method = "Berg" +and method = "Berg2":

    CvM, KS, AD

    test statistic according to the choice of statistic

    @@ -169,10 +167,8 @@

    Value

    p.value

    bootstrapped p-value

    -


    - - -

    Warning: The code for all the p-values are not yet approved since some of them are +


    +Warning: The code for all the p-values are not yet approved since some of them are moved from R-code to C-code. If you need p-values the best way is to write your own algorithm as suggested in Schepsmeier (2013) to get bootstrapped p-values.

    @@ -332,15 +328,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVineGrad.html b/docs/reference/RVineGrad.html index 3dd2fb9..d0fce9e 100644 --- a/docs/reference/RVineGrad.html +++ b/docs/reference/RVineGrad.html @@ -5,7 +5,7 @@ - +
    @@ -33,14 +33,14 @@
    - +
    @@ -69,15 +69,17 @@

    Gradient of the Log-Likelihood of an R-Vine Copula Model

    Arguments

    -
    data
    + + +
    data

    An N x d data matrix (with uniform margins).

    -
    RVM
    +
    RVM

    An RVineMatrix() object including the structure and the pair-copula families and parameters.
    Only the following copula -families are allowed in RVM$family
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; ``survival Joe'')
    23 = rotated Clayton copula (90 degrees)
    +families are allowed in RVM$family
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; “survival Joe”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `33` = rotated Clayton copula (270 degrees)
    @@ -85,35 +87,31 @@

    Arguments

    `36` = rotated Joe copula (270 degrees)

    -
    par
    +
    par

    A d x d matrix with the pair-copula parameters (optional; default: par = RVM$par).

    -
    par2
    +
    par2

    A d x d matrix with the second parameters of pair-copula families with two parameters (optional; default: par2 = RVM$par2).

    -
    start.V
    +
    start.V

    Transformations (h-functions and log-likelihoods of each pair-copula) of previous calculations (see output; default: start.V = NA).

    -
    posParams
    +
    posParams

    A d x d matrix indicating which copula has to be considered in the gradient (default: posParams = (RVM$family > 0)).

    Value

    - - -

    gradient The calculated gradient of the log-likelihood value -of the R-vine copula model. (three matrices: direct, indirect

    - - -

    and value).

    +

    gradient The calculated gradient of the log-likelihood value +of the R-vine copula model. (three matrices: direct, indirect +and value).

    Details

    @@ -220,15 +218,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVineHessian.html b/docs/reference/RVineHessian.html index b4a98eb..72b3370 100644 --- a/docs/reference/RVineHessian.html +++ b/docs/reference/RVineHessian.html @@ -5,7 +5,7 @@ - +
    @@ -33,14 +33,14 @@
    - +
    @@ -62,15 +62,17 @@

    Hessian Matrix of the Log-Likelihood of an R-Vine Copula Model

    Arguments

    -
    data
    + + +
    data

    An N x d data matrix (with uniform margins).

    -
    RVM
    +
    RVM

    An RVineMatrix() object including the structure, the pair-copula families, and the parameters.
    Only the following copula -families are allowed in RVM$family
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; ``survival Joe'')
    23 = rotated Clayton copula (90 degrees)
    +families are allowed in RVM$family
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; “survival Joe”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `33` = rotated Clayton copula (270 degrees)
    @@ -80,7 +82,9 @@

    Arguments

    Value

    -
    hessian
    + + +
    hessian

    The calculated Hessian matrix of the log-likelihood value of the R-vine copula model.

    @@ -203,15 +207,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVineLogLik.html b/docs/reference/RVineLogLik.html index 525743a..1a10c40 100644 --- a/docs/reference/RVineLogLik.html +++ b/docs/reference/RVineLogLik.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -69,42 +69,44 @@

    Log-Likelihood of an R-Vine Copula Model

    Arguments

    -
    data
    + + +
    data

    An N x d data matrix (with uniform margins).

    -
    RVM
    +
    RVM

    An RVineMatrix() object including the structure and the pair-copula families and parameters.

    -
    par
    +
    par

    A d x d matrix with the pair-copula parameters (optional; default: par = RVM$par).

    -
    par2
    +
    par2

    A d x d matrix with the second parameters of pair-copula families with two parameters (optional; default: par2 = RVM$par2).

    -
    separate
    +
    separate

    Logical; whether log-likelihoods are returned point wisely (default: separate = FALSE).

    -
    verbose
    +
    verbose

    In case something goes wrong, additional output will be plotted.

    -
    check.pars
    +
    check.pars

    logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

    -
    calculate.V
    +
    calculate.V

    logical; whether V matrices should be calculated. Default is TRUE, but requires a lot of memory when dimension is large. Use FALSE for a memory efficient version.

    @@ -112,7 +114,9 @@

    Arguments

    Value

    -
    loglik
    + + +
    loglik

    The calculated log-likelihood value of the R-vine copula model.

    V
    @@ -287,15 +291,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVineMLE.html b/docs/reference/RVineMLE.html index 9e35ca6..bb16aff 100644 --- a/docs/reference/RVineMLE.html +++ b/docs/reference/RVineMLE.html @@ -5,7 +5,7 @@ - +
    @@ -33,14 +33,14 @@
    - +
    @@ -74,64 +74,66 @@

    Maximum Likelihood Estimation of an R-Vine Copula Model

    Arguments

    -
    data
    + + +
    data

    An N x d data matrix (with uniform margins).

    -
    RVM
    +
    RVM

    An RVineMatrix() object including the structure and the pair-copula families and parameters (if known).

    -
    start
    +
    start

    Lower triangular d x d matrix with zero diagonal entries with starting values for the pair-copula parameters (optional; otherwise they are calculated via
    RVineSeqEst(); default: start = RVM$par).

    -
    start2
    +
    start2

    Lower triangular d x d matrix with zero diagonal entries with starting values for the second parameters of pair-copula families with two parameters (optional; otherwise they are calculated via RVineSeqEst(); default: start2 = RVM$par2).

    -
    maxit
    +
    maxit

    The maximum number of iteration steps (optional; default: maxit = 200).

    -
    max.df
    +
    max.df

    Numeric; upper bound for the estimation of the degrees of freedom parameter of the t-copula (default: max.df = 30; for more details see BiCopEst()).

    -
    max.BB
    +
    max.BB

    List; upper bounds for the estimation of the two parameters (in absolute values) of the BB1, BB6, BB7 and BB8 copulas
    (default: max.BB = list(BB1=c(5,6),BB6=c(6,6),BB7=c(5,6),BB8=c(6,1))).

    -
    grad
    +
    grad

    If RVM$family only contains one parameter copula families or the t-copula the analytical gradient can be used for maximization of the log-likelihood (see RVineGrad(); default: grad = FALSE).

    -
    hessian
    +
    hessian

    Logical; whether the Hessian matrix of parameter estimates is estimated (default: hessian = FALSE). Note that this is not the Hessian Matrix calculated via RVineHessian() but via finite differences.

    -
    se
    +
    se

    Logical; whether standard errors of parameter estimates are estimated on the basis of the Hessian matrix (see above; default: se = FALSE).

    -
    ...
    +
    ...

    Further arguments for optim (e.g. factr controls the convergence of the "L-BFGS-B" method, or trace, a non-negative integer, determines if tracing information on the progress of the @@ -141,7 +143,9 @@

    Arguments

    Value

    -
    RVM
    + + +
    RVM

    RVineMatrix() object with the calculated parameters stored in RVM$par and RVM$par2. Additional information about the fit is added (e.g., log-likelihood, AIC, BIC).

    @@ -263,15 +267,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVineMatrix.html b/docs/reference/RVineMatrix.html index 2213bc5..b21d0c5 100644 --- a/docs/reference/RVineMatrix.html +++ b/docs/reference/RVineMatrix.html @@ -6,7 +6,7 @@ - +
    @@ -34,14 +34,14 @@
    - +
    @@ -71,16 +71,18 @@

    R-Vine Copula Model in Matrix Notation

    Arguments

    -
    Matrix
    + + +
    Matrix

    Lower (or upper) triangular d x d matrix that defines the R-vine tree structure.

    -
    family
    +
    family

    Lower (or upper) triangular d x d matrix with zero diagonal entries that assigns the pair-copula families to each (conditional) pair defined by Matrix (default: family = array(0,dim=dim(Matrix))). The bivariate copula families are defined as -follows:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7'')
    20 = rotated BB8 copula (180 degrees; ``survival BB8'')
    23 = rotated Clayton copula (90 degrees)
    +follows:
    0 = independence copula
    1 = Gaussian copula
    2 = Student t copula (t-copula)
    3 = Clayton copula
    4 = Gumbel copula
    5 = Frank copula
    6 = Joe copula
    7 = BB1 copula
    8 = BB6 copula
    9 = BB7 copula
    10 = BB8 copula
    13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
    16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
    18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
    20 = rotated BB8 copula (180 degrees; “survival BB8”)
    23 = rotated Clayton copula (90 degrees)
    `24` = rotated Gumbel copula (90 degrees)
    `26` = rotated Joe copula (90 degrees)
    `27` = rotated BB1 copula (90 degrees)
    @@ -104,24 +106,24 @@

    Arguments

    `234` = rotated Tawn type 2 copula (270 degrees)

    -
    par
    +
    par

    Lower (or upper) triangular d x d matrix with zero diagonal entries that assigns the (first) pair-copula parameter to each (conditional) pair defined by Matrix
    (default: par = array(NA, dim = dim(Matrix))).

    -
    par2
    +
    par2

    Lower (or upper) triangular d x d matrix with zero diagonal entries that assigns the second parameter for pair-copula families with two parameters to each (conditional) pair defined by Matrix (default: par2 = array(NA, dim = dim(Matrix))).

    -
    names
    +
    names

    A vector of names for the d variables; default: names = NULL.

    -
    check.pars
    +
    check.pars

    logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

    @@ -129,9 +131,7 @@

    Arguments

    Value

    - - -

    An object of class RVineMatrix(), i.e., a list with the +

    An object of class RVineMatrix(), i.e., a list with the following components:

    Matrix

    R-vine tree structure matrix.

    @@ -169,10 +169,8 @@

    Value

    Blomqvist's beta matrix.

    Objects of this class are also returned by the RVineSeqEst(), -RVineCopSelect(), and RVineStructureSelect()

    - - -

    functions. In this case, further information about the fit is added.

    +RVineCopSelect(), and RVineStructureSelect() +functions. In this case, further information about the fit is added.

    Note

    @@ -274,7 +272,7 @@

    Examples

    #> 1 <-> V1, 2 <-> V2, 3 <-> V3, 4 <-> V4, 5 <-> V5 ## inspect the model using plots -if (FALSE) plot(RVM) # tree structure +if (FALSE) plot(RVM) # tree structure # \dontrun{} contour(RVM) # contour plots of all pair-copulas @@ -296,15 +294,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVineMatrixCheck.html b/docs/reference/RVineMatrixCheck.html index 7c189e9..61c15af 100644 --- a/docs/reference/RVineMatrixCheck.html +++ b/docs/reference/RVineMatrixCheck.html @@ -3,7 +3,7 @@ - +
    @@ -31,14 +31,14 @@
    - +
    @@ -58,13 +58,17 @@

    R-Vine Matrix Check

    Arguments

    -
    M
    + + +
    M

    A \(dxd\) vine matrix.

    Value

    -
    code
    + + +
    code

    1 for OK;
    -4 matrix is neither lower nor upper triangular;
    -3 diagonal can not be put in order d:1;
    -2 for not permutation of j:d in column d-j;
    -1 if cannot find proper binary array from array in natural order.

    @@ -81,7 +85,7 @@

    Note

    References

    Joe H, Cooke RM and Kurowicka D (2011). Regular vines: generation algorithm and number of equivalence classes. In Dependence -Modeling: Vine Copula Handbook, pp 219--231. World Scientific, Singapore.

    +Modeling: Vine Copula Handbook, pp 219–231. World Scientific, Singapore.

    See also

    @@ -139,15 +143,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVineMatrixNormalize.html b/docs/reference/RVineMatrixNormalize.html index 819df6a..9715896 100644 --- a/docs/reference/RVineMatrixNormalize.html +++ b/docs/reference/RVineMatrixNormalize.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,13 +60,17 @@

    Normalization of R-Vine Matrix

    Arguments

    -
    RVM
    + + +
    RVM

    RVineMatrix() defining the R-vine structure

    Value

    -
    RVM
    + + +
    RVM

    An RVineMatrix() in natural ordering with entries in RVM$names keeping track of the reordering.

    @@ -129,15 +133,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVineMatrixSample.html b/docs/reference/RVineMatrixSample.html index c1ee5cc..6460d95 100644 --- a/docs/reference/RVineMatrixSample.html +++ b/docs/reference/RVineMatrixSample.html @@ -3,7 +3,7 @@ - +
    @@ -31,14 +31,14 @@
    - +
    @@ -58,24 +58,24 @@

    Random sampling of R-Vine matrices

    Arguments

    -
    d
    + + +
    d

    Dimension of the R-Vine matrices.

    -
    size
    +
    size

    Number of matrices to sample.

    -
    naturalOrder
    +
    naturalOrder

    Should the matrices be in the natural order (default: naturalOrder = FALSE).

    Value

    - - -

    A list of length size with each element containing one +

    A list of length size with each element containing one R-Vine matrix.

    @@ -88,7 +88,7 @@

    Note

    References

    Joe H, Cooke RM and Kurowicka D (2011). Regular vines: generation algorithm and number of equivalence classes. In Dependence -Modeling: Vine Copula Handbook, pp 219--231. World Scientific, Singapore.

    +Modeling: Vine Copula Handbook, pp 219–231. World Scientific, Singapore.

    See also

    @@ -129,15 +129,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVinePDF.html b/docs/reference/RVinePDF.html index 5f774f1..1294b58 100644 --- a/docs/reference/RVinePDF.html +++ b/docs/reference/RVinePDF.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,17 +60,19 @@

    PDF of an R-Vine Copula Model

    Arguments

    -
    newdata
    + + +
    newdata

    An N x d data matrix that specifies where the density shall be evaluated.

    -
    RVM
    +
    RVM

    An RVineMatrix() object including the structure and the pair-copula families and parameters.

    -
    verbose
    +
    verbose

    In case something goes wrong, additional output will be plotted.

    @@ -168,15 +170,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVinePIT.html b/docs/reference/RVinePIT.html index 96903db..f8dc523 100644 --- a/docs/reference/RVinePIT.html +++ b/docs/reference/RVinePIT.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,19 +60,19 @@

    Probability Integral Transformation for R-Vine Copula Models

    Arguments

    -
    data
    + + +
    data

    An N x d data matrix (with uniform margins).

    -
    RVM
    +
    RVM

    RVineMatrix() objects of the R-vine model.

    Value

    - - -

    An N x d matrix of PIT data from the given R-vine copula +

    An N x d matrix of PIT data from the given R-vine copula model.

    @@ -144,15 +144,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVinePar2Beta.html b/docs/reference/RVinePar2Beta.html index 3e8c99c..404a7e7 100644 --- a/docs/reference/RVinePar2Beta.html +++ b/docs/reference/RVinePar2Beta.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,22 +60,22 @@

    Blomqvist's Beta Values of an R-Vine Copula Model

    Arguments

    -
    RVM
    + + +
    RVM

    An RVineMatrix() object.
    Note that the Student's t-copula is not allowed since the CDF of the t-copula is not implemented (see BiCopCDF() and BiCopPar2Beta()).

    -
    check.pars
    +
    check.pars

    logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

    Value

    - - -

    Matrix with the same structure as the family and parameter matrices +

    Matrix with the same structure as the family and parameter matrices of the RVineMatrix() object RVM where the entries are values of Blomqvist's beta corresponding to the families and parameters of the R-vine copula model given by RVM.

    @@ -140,15 +140,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVinePar2Tau.html b/docs/reference/RVinePar2Tau.html index f2d4a61..c477654 100644 --- a/docs/reference/RVinePar2Tau.html +++ b/docs/reference/RVinePar2Tau.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,20 +60,20 @@

    Kendall's Tau Values of an R-Vine Copula Model

    Arguments

    -
    RVM
    + + +
    RVM

    An RVineMatrix() object.

    -
    check.pars
    +
    check.pars

    logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

    Value

    - - -

    Matrix with the same structure as the family and parameter matrices +

    Matrix with the same structure as the family and parameter matrices of the RVineMatrix() object RVM where the entries are values of Kendall's tau corresponding to the families and parameters of the R-vine copula model given by RVM.

    @@ -139,15 +139,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVineSeqEst.html b/docs/reference/RVineSeqEst.html index 581a3c9..02fa166 100644 --- a/docs/reference/RVineSeqEst.html +++ b/docs/reference/RVineSeqEst.html @@ -5,7 +5,7 @@ - +
    @@ -33,14 +33,14 @@
    - +
    @@ -72,16 +72,18 @@

    Sequential Estimation of an R-Vine Copula Model

    Arguments

    -
    data
    + + +
    data

    An N x d data matrix (with uniform margins).

    -
    RVM
    +
    RVM

    An RVineMatrix() object including the structure, the pair-copula families and the pair-copula parameters (if they are known).

    -
    method
    +
    method

    indicates the estimation method: either maximum likelihood estimation (method = "mle"; default) or inversion of Kendall's tau (method = "itau"). For method = "itau" only @@ -90,32 +92,32 @@

    Arguments

    interval (2, 10].

    -
    se
    +
    se

    Logical; whether standard errors are estimated (default: se = FALSE).

    -
    max.df
    +
    max.df

    Numeric; upper bound for the estimation of the degrees of freedom parameter of the t-copula (default: max.df = 30; for more details see BiCopEst()).

    -
    max.BB
    +
    max.BB

    List; upper bounds for the estimation of the two parameters (in absolute values) of the BB1, BB6, BB7 and BB8 copulas
    (default: max.BB = list(BB1=c(5,6),BB6=c(6,6),BB7=c(5,6),BB8=c(6,1))).

    -
    progress
    +
    progress

    Logical; whether the pairwise estimation progress is printed (default: progress = FALSE).

    -
    weights
    +
    weights

    Numerical; weights for each observation (optional).

    -
    cores
    +
    cores

    integer; if cores > 1, estimation will be parallelized within each tree (using parallel::parLapply()). However, the overhead caused by parallelization is likely to make the function run slower @@ -124,9 +126,7 @@

    Arguments

    Value

    - - -

    An RVineMatrix() object with the sequentially +

    An RVineMatrix() object with the sequentially estimated parameters stored in RVM$par and RVM$par2. The object is augmented by the following information about the fit:

    se, se2
    @@ -266,15 +266,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVineSim.html b/docs/reference/RVineSim.html index d82d073..7e97a95 100644 --- a/docs/reference/RVineSim.html +++ b/docs/reference/RVineSim.html @@ -3,7 +3,7 @@ - +
    @@ -31,14 +31,14 @@
    - +
    @@ -58,27 +58,27 @@

    Simulation from an R-Vine Copula Model

    Arguments

    -
    N
    + + +
    N

    Number of d-dimensional observations to simulate.

    -
    RVM
    +
    RVM

    An RVineMatrix() object containing the information of the R-vine copula model. Optionally, a length-N list of RVineMatrix() objects sharing the same structure, but possibly different family/parameter can be supplied.

    -
    U
    +
    U

    If not NULL(), an (N,d)-matrix of \(U[0,1]\) random variates to be transformed to the copula sample.

    Value

    - - -

    An N x d matrix of data simulated from the given R-vine +

    An N x d matrix of data simulated from the given R-vine copula model.

    @@ -149,15 +149,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVineStdError.html b/docs/reference/RVineStdError.html index 8d2db21..998b05a 100644 --- a/docs/reference/RVineStdError.html +++ b/docs/reference/RVineStdError.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,18 +60,22 @@

    Standard Errors of an R-Vine Copula Model

    Arguments

    -
    hessian
    + + +
    hessian

    The Hessian matrix of the given R-vine.

    -
    RVM
    +
    RVM

    An RVineMatrix() object including the structure, the pair-copula families, and the parameters.

    Value

    -
    se
    + + +
    se

    The calculated standard errors for the first parameter matrix. The entries are ordered with respect to the ordering of the RVM$par matrix.

    @@ -187,15 +191,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVineStructureSelect.html b/docs/reference/RVineStructureSelect.html index 4db1f19..8cb1352 100644 --- a/docs/reference/RVineStructureSelect.html +++ b/docs/reference/RVineStructureSelect.html @@ -6,7 +6,7 @@ - +
    @@ -34,14 +34,14 @@
    - +
    @@ -80,11 +80,13 @@

    Sequential Specification of R- and C-Vine Copula Models

    Arguments

    -
    data
    + + +
    data

    An N x d data matrix (with uniform margins).

    -
    familyset
    +
    familyset

    An integer vector of pair-copula families to select from. The vector has to include at least one pair-copula family that allows for positive and one that allows for negative @@ -94,7 +96,7 @@

    Arguments

    as in BiCop().

    -
    type
    +
    type

    Type of the vine model to be specified:
    0 or "RVine" = R-vine (default)
    1 or "CVine" = C-vine
    C- and D-vine copula models with pre-specified order can be specified using CDVineCopSelect of the package CDVine. Similarly, R-vine copula @@ -102,13 +104,13 @@

    Arguments

    RVineCopSelect().

    -
    selectioncrit
    +
    selectioncrit

    Character indicating the criterion for pair-copula selection. Possible choices:selectioncrit = "AIC" (default), "BIC", or "logLik" (see BiCopSelect()).

    -
    indeptest
    +
    indeptest

    logical; whether a hypothesis test for the independence of u1 and u2 is performed before bivariate copula selection (default: indeptest = FALSE; see BiCopIndTest()). The @@ -116,45 +118,45 @@

    Arguments

    hypothesis of independence cannot be rejected.

    -
    level
    +
    level

    numeric; significance level of the independence test (default: level = 0.05).

    -
    trunclevel
    +
    trunclevel

    integer; level of truncation.

    -
    progress
    +
    progress

    logical; whether the tree-wise specification progress is printed (default: progress = FALSE).

    -
    weights
    +
    weights

    numeric; weights for each observation (optional).

    -
    treecrit
    +
    treecrit

    edge weight for Dissman's structure selection algorithm, see Details.

    -
    rotations
    +
    rotations

    If TRUE, all rotations of the families in familyset are included.

    -
    se
    +
    se

    Logical; whether standard errors are estimated (default: se = FALSE).

    -
    presel
    +
    presel

    Logical; whether to exclude families before fitting based on symmetry properties of the data. Makes the selection about 30\ (on average), but may yield slightly worse results in few special cases.

    -
    method
    +
    method

    indicates the estimation method: either maximum likelihood estimation (method = "mle"; default) or inversion of Kendall's tau (method = "itau"). For method = "itau" only @@ -163,7 +165,7 @@

    Arguments

    interval (2, 10].

    -
    cores
    +
    cores

    integer; if cores > 1, estimation will be parallelized within each tree (using parallel::parLapply()). Note that parallelization causes substantial overhead and may be slower than @@ -173,9 +175,7 @@

    Arguments

    Value

    - - -

    An RVineMatrix() object with the selected structure +

    An RVineMatrix() object with the selected structure (RVM$Matrix) and families (RVM$family) as well as sequentially estimated parameters stored in RVM$par and RVM$par2. The object is augmented by the following information about the fit:

    @@ -318,7 +318,7 @@

    Examples

    #> 1 <-> ALV.DE, 2 <-> BAS.DE, 3 <-> BAYN.DE, 4 <-> BMW.DE ## inspect the fitted model using plots -if (FALSE) plot(RVM) # tree structure +if (FALSE) plot(RVM) # tree structure # \dontrun{} contour(RVM) # contour plots of all pair-copulas @@ -365,15 +365,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVineTreePlot.html b/docs/reference/RVineTreePlot.html index 712983d..cb03520 100644 --- a/docs/reference/RVineTreePlot.html +++ b/docs/reference/RVineTreePlot.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -68,22 +68,24 @@

    Visualization of R-Vine Tree Structure

    Arguments

    -
    x
    + + +
    x

    RVineMatrix object.

    -
    tree
    +
    tree

    "ALL" or integer vector; specifies which trees are plotted.

    -
    type
    +
    type

    integer; specifies how to make use of variable names:
    0 = variable names are ignored,
    1 = variable names are used to annotate vertices,
    2 = uses numbers in plot and adds a legend for variable names.

    -
    edge.labels
    +
    edge.labels

    character; either a vector of edge labels or one of the following:
    "family" = pair-copula family abbreviation (see BiCopName()),
    "par" = @@ -92,17 +94,17 @@

    Arguments

    parameters
    "family-tau" = pair-copula family and Kendall's tau.

    -
    legend.pos
    +
    legend.pos

    the x argument for graphics::legend().

    -
    interactive
    +
    interactive

    logical; if TRUE, the user is asked to adjust the positioning of vertices with his mouse.

    -
    ...
    +
    ...

    Arguments passed to network::plot.network().

    @@ -128,15 +130,15 @@

    Author

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/RVineVuongTest.html b/docs/reference/RVineVuongTest.html index dc40e3b..549af12 100644 --- a/docs/reference/RVineVuongTest.html +++ b/docs/reference/RVineVuongTest.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,17 +60,21 @@

    Vuong Test Comparing Two R-Vine Copula Models

    Arguments

    -
    data
    + + +
    data

    An N x d data matrix (with uniform margins).

    -
    RVM1, RVM2
    +
    RVM1, RVM2

    RVineMatrix() objects of models 1 and 2.

    Value

    -
    statistic, statistic.Akaike, statistic.Schwarz
    + + +
    statistic, statistic.Akaike, statistic.Schwarz

    Test statistics without correction, with Akaike correction and with Schwarz correction.

    @@ -162,15 +166,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/TauMatrix.html b/docs/reference/TauMatrix.html index 0867eb3..00943f5 100644 --- a/docs/reference/TauMatrix.html +++ b/docs/reference/TauMatrix.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,19 +60,19 @@

    Matrix of Empirical Kendall's Tau Values

    Arguments

    -
    data
    + + +
    data

    An N x d data matrix.

    -
    weights
    +
    weights

    Numerical; weights for each observation (optional).

    Value

    - - -

    Matrix of the empirical Kendall's taus.

    +

    Matrix of the empirical Kendall's taus.

    References

    @@ -161,15 +161,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/VC2copula-deprecated.html b/docs/reference/VC2copula-deprecated.html index ebbad95..3e366a6 100644 --- a/docs/reference/VC2copula-deprecated.html +++ b/docs/reference/VC2copula-deprecated.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -130,27 +130,29 @@

    Deprecated

    Arguments

    -
    family
    + + +
    family

    ..

    -
    par
    +
    par

    ...

    -
    par2
    +
    par2

    ...

    -
    param
    +
    param

    ...

    -
    RVM
    +
    RVM

    ...

    -
    type
    +
    type

    ...

    @@ -167,15 +169,15 @@

    Arguments

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/VineCopula-package.html b/docs/reference/VineCopula-package.html index 13600ee..fdfb831 100644 --- a/docs/reference/VineCopula-package.html +++ b/docs/reference/VineCopula-package.html @@ -1,6 +1,6 @@ -Statistical Inference of Vine Copulas — VineCopula-package • VineCopulaStatistical Inference of Vine Copulas — VineCopula-package • VineCopula - +
    @@ -37,14 +37,14 @@
    - +
    @@ -55,8 +55,8 @@

    Statistical Inference of Vine Copulas

    -

    Provides tools for the statistical analysis of regular vine copula - models, see Aas et al. (2009) <doi:10.1016/j.insmatheco.2007.02.001> and +

    Provides tools for the statistical analysis of regular vine copula + models, see Aas et al. (2009) <doi:10.1016/j.insmatheco.2007.02.001> and Dissman et al. (2013) <doi:10.1016/j.csda.2012.08.010>. The package includes tools for parameter estimation, model selection, simulation, goodness-of-fit tests, and visualization. Tools for estimation, @@ -174,15 +174,15 @@

    Author

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/as.copuladata.html b/docs/reference/as.copuladata.html index dc6fce6..c58863d 100644 --- a/docs/reference/as.copuladata.html +++ b/docs/reference/as.copuladata.html @@ -4,7 +4,7 @@ - +
    @@ -32,14 +32,14 @@
    - +
    @@ -60,7 +60,9 @@

    Copula Data Objects

    Arguments

    -
    data
    + + +
    data

    Either a data.frame, a matrix or a list containing copula data (i.e. data with uniform margins on \([0,1]\)). The list elements have to be vectors of identical length.

    @@ -107,15 +109,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/daxreturns.html b/docs/reference/daxreturns.html index a022563..09344e1 100644 --- a/docs/reference/daxreturns.html +++ b/docs/reference/daxreturns.html @@ -6,7 +6,7 @@ - +
    @@ -34,14 +34,14 @@
    - +
    @@ -144,15 +144,15 @@

    Examples

    -

    Site built with pkgdown 2.0.9.

    +

    Site built with pkgdown 2.1.1.

    - - + + diff --git a/docs/reference/index.html b/docs/reference/index.html index 23d5ac4..0014cd7 100644 --- a/docs/reference/index.html +++ b/docs/reference/index.html @@ -1,9 +1,9 @@ -Function reference • VineCopulaPackage index • VineCopula - +
    @@ -31,14 +31,14 @@
    - +
    @@ -186,6 +186,10 @@

    All functions RVineAIC() RVineBIC()

    AIC and BIC of an R-Vine Copula Model

    +

    RVineCDF()

    +

    CDF of an R-Vine Copula Model

    RVineClarkeTest()