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Python Module approxQoEdist

A script is provided which approximates a QoE distribution with a Beta distribution for given MOS and SOS parameter. More details on the background and a detailed description is provided in the paper [QoEMAN2020].

This tool is published under the license CC BY-SA 4.0 at https://github.com/hossfeld/approx-qoe-distribution

The following paper is to be cited in the bibliography whenever the tool is used. [QoEMAN2020] Tobias Hossfeld, Poul E. Heegaard, Martin Varela, Lea Skorin-Kapov, Markus Fiedler. "From QoS Distributions to QoE Distributions: a System's Perspective". 4th International Workshop on Quality of Experience Management (QoE Management 2020), featured by IEEE Conference on Network Softwarization (IEEE NetSoft 2020), Ghent, Belgium.

Created on Thu Mar 26 21:51:00 2020 @author: Tobias Hossfeld

calcSOSParameterForMOSSOS

calcSOSParameterForMOSSOS(mos, sos, low=1, high=5)

Derives SOS parameter a from a numpy array of MOS values and SOS values.

Parameters:

  • mos (numpy.ndarray): Array of MOS values for different conditions.
  • sos (numpy.ndarray): Array of the SOS values corresponding for the related MOS value.
  • low (float): Lower bound of the rating scale used for the ratings, e.g. low=1 for a 5-point scale.
  • high (float): Upper bound of the rating scale used for the ratings, e.g. high=5 for a 5-point scale.

Returns:

  • float: SOS parameter a

See also: Tobias Hossfeld, Poul E. Heegaard, Martin Varela, Sebastian Moeller. "QoE beyond the MOS: an in-depth look at QoE via better metrics and their relation to MOS." Quality and User Experience, 1, 2 (2016). https://doi.org/10.1007/s41233-016-0002-1

calcSOSParameter

calcSOSParameter(y, low=1, high=5)

Derives SOS parameter a from subjective measurements provided as Pandas dataframe or Numpy ndarray.

Parameters:

  • y (numpy.ndarray or pandas.DataFrame): QoE ratings on a scale from [low;high] which may be provided as Numpy array or as a Pandas dataframe. If y is a matrix, each row i represents the ratings all users for test condition i. Each column j represents the ratings from user j for all conditions. y[i,j] provides the rating of user j for test condition i. y has dimension conditions x user_ratings. If y is a Pandas dataframe, it must consist a column 'rating' and a column 'condition'. Each individual 'rating' is provided as a separate entry for the particular 'condition'.
  • low (float): Lower bound of the rating scale used for the ratings, e.g. low=1 for a 5-point scale.
  • high (float): Upper bound of the rating scale used for the ratings, e.g. high=5 for a 5-point scale.

Returns:

  • float: SOS parameter a

Raises:

  • TypeError: If y is not provided as Numpy array or Pandas DataFrame

getBetaParamsForMOSSOS

getBetaParamsForMOSSOS(mos, sos, low=1, high=5)

Returns the parameters of the Beta distribuiton given MOS and SOS on [low;high] rating scale.

Parameters:

  • mos (float): Mean Opinion Score on the [low;high] rating scale.
  • sos (float): Standard Deviation of Opinion Scores on the [low;high] rating scale.
  • low (float): Lower bound of the rating scale used for the ratings, e.g. low=1 for a 5-point scale.
  • high (float): Upper bound of the rating scale used for the ratings, e.g. high=5 for a 5-point scale.

Returns:

  • (float, float): Tuple (a,b) of the parameters of the Beta distribution

Raises:

  • ValueError: If maximum SOS is exceeded for given MOS. If MOS is not in range [low;high].

See also: Tobias Hossfeld, Raimund Schatz, Sebastian Egger. "SOS: The MOS is not enough!." 2011 Quality of Multimedia Experience (QoMEX 2011). IEEE, 2011. https://doi.org/10.1109/QoMEX.2011.6065690

checkParameters

checkParameters(mos, sos_parameter=0.25, low=1, high=5)

Checks the input parameters if they are valid and potentially raises exceptions.

Parameters:

  • mos (float): Mean Opinion Score on the [low;high] rating scale.
  • sos_parameter (float): SOS parameter is scale independent and must be in the range [0;1].
  • low (float): Lower bound of the rating scale used for the ratings, e.g. low=1 for a 5-point scale.
  • high (float): Upper bound of the rating scale used for the ratings, e.g. high=5 for a 5-point scale.

Raises:

  • ValueError: If SOS parameter is not in range [0;1]. If upper bound 'high' of rating scale is smaller than the lower bound 'low'. If MOS is not in range [low;high].

getBetaParams

getBetaParams(mos, sos_parameter=0.25, low=1, high=5)

Returns the parameters of the Beta distribuiton given MOS and SOS parameter on [low;high] rating scale.

Parameters:

  • mos (float): Mean Opinion Score on the [low;high] rating scale.
  • sos_parameter (float): SOS parameter is scale independent and must be in the range [0;1].
  • low (float): Lower bound of the rating scale used for the ratings, e.g. low=1 for a 5-point scale.
  • high (float): Upper bound of the rating scale used for the ratings, e.g. high=5 for a 5-point scale.

Returns:

  • (float, float): Tuple (a,b) of the parameters of the Beta distribution

Raises:

  • ValueError: If SOS parameter is not in range [0;1]. If upper bound 'high' of rating scale is smaller than the lower bound 'low'. If MOS is not in range [low;high].

getBetaCDF

getBetaCDF(x, mos, sos_parameter=0.25, low=1, high=5)

Returns the CDF value P(X <= x) of the Beta distribution X approximating the rating distribution given MOS and SOS parameter on [low;high] rating scale.

Parameters:

  • x (float): Threshold of the user rating. The probability P(X <= x) is computed using the Beta distribution approximation, i.e. the probability that the user rating is smaller than x for given MOS and SOS parameter on the [low;high] rating scale.
  • mos (float): Mean Opinion Score on the [low;high] rating scale.
  • sos_parameter (float): SOS parameter is scale independent and must be in the range [0;1].
  • low (float): Lower bound of the rating scale used for the ratings, e.g. low=1 for a 5-point scale.
  • high (float): Upper bound of the rating scale used for the ratings, e.g. high=5 for a 5-point scale.

Returns:

  • float: CDF value P(X <= x) of the Beta distribuiton X approximation.

Raises:

  • ValueError: If SOS parameter is not in range [0;1]. If upper bound 'high' of rating scale is smaller than the lower bound 'low'. If MOS or x is not in range [low;high].

getBetaPDF

getBetaPDF(x, mos, sos_parameter=0.25, low=1, high=5)

Returns the PDF value at x of the Beta distribution X approximating the rating distribution given MOS and SOS parameter on [low;high] rating scale.

Parameters:

  • x (float): Threshold of the user rating. The PDF at x is computed using the Beta distribution approximation.
  • mos (float): Mean Opinion Score on the [low;high] rating scale.
  • sos_parameter (float): SOS parameter is scale independent and must be in the range [0;1].
  • low (float): Lower bound of the rating scale used for the ratings, e.g. low=1 for a 5-point scale.
  • high (float): Upper bound of the rating scale used for the ratings, e.g. high=5 for a 5-point scale.

Returns:

  • float: PDF value at x of the Beta distribuiton X approximation.

Raises:

  • ValueError: If SOS parameter is not in range [0;1]. If upper bound 'high' of rating scale is smaller than the lower bound 'low'. If MOS or x is not in range [low;high].

getBetaDistribution

getBetaDistribution(mos, sos_parameter=0.25, low=1, high=5)

Returns the Beta distribution X approximating the rating distribution given MOS and SOS parameter on [low;high] rating scale.

Parameters:

  • mos (float): Mean Opinion Score on the [low;high] rating scale.
  • sos_parameter (float): SOS parameter is scale independent and must be in the range [0;1].
  • low (float): Lower bound of the rating scale used for the ratings, e.g. low=1 for a 5-point scale.
  • high (float): Upper bound of the rating scale used for the ratings, e.g. high=5 for a 5-point scale.

Returns:

  • scipy.stats.beta: Beta distribution approximation

Raises:

  • ValueError: If SOS parameter is not in range [0;1]. If upper bound 'high' of rating scale is smaller than the lower bound 'low'. If MOS or x is not in range [low;high].

getDiscreteDistribution

getDiscreteDistribution(mos, sos_parameter=0.25, low=1, high=5)

Returns the discrete distribution X approximating the rating distribution given MOS and SOS parameter on a discrete rating scale from low to high.

Parameters:

  • mos (float): Mean Opinion Score on the [low;high] rating scale.
  • sos_parameter (float): SOS parameter is scale independent and must be in the range [0;1].
  • low (float): Lower bound of the rating scale used for the ratings, e.g. low=1 for a 5-point scale.
  • high (float): Upper bound of the rating scale used for the ratings, e.g. high=5 for a 5-point scale.

Returns:

  • scipy.stats.rv_discrete: discrete distribution based on Beta approximation

Raises:

  • ValueError: If SOS parameter is not in range [0;1]. If upper bound 'high' of rating scale is smaller than the lower bound 'low'. If MOS or x is not in range [low;high].