README.md

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Kurtosis

F distribution excess kurtosis.

The excess kurtosis for a F random variable with numerator degrees of freedom d1 and denominator degrees of freedom d2 is

$$\mathop{\mathrm{Kurt}}\left( X \right) = \gamma_{2}=12{\frac{d_{1}(5d_{2}-22)(d_{1}+d_{2}-2)+(d_{2}-4)(d_{2}-2)^{2}}{d_{1}(d_{2}-6)(d_{2}-8)(d_{1}+d_{2}-2)}}.$$

for d1 > 0 and d2 > 8. Otherwise, the kurtosis is not defined.

Usage

import kurtosis from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-f-kurtosis@deno/mod.js';

kurtosis( d1, d2 )

Returns the excess kurtosis of an F distribution with parameters d1 (numerator degrees of freedom) and d2 (denominator degrees of freedom).

var v = kurtosis( 4.0, 9.0 );
// returns ~114.273

v = kurtosis( 4.0, 12.0 );
// returns ~26.143

v = kurtosis( 8.0, 9.0 );
// returns ~100.167

If provided NaN as any argument, the function returns NaN.

var v = kurtosis( NaN, 7.0 );
// returns NaN

v = kurtosis( 3.0, NaN );
// returns NaN

If provided d1 <= 0, the function returns NaN.

var v = kurtosis( 0.0, 9.0 );
// returns NaN

v = kurtosis( -1.0, 9.0 );
// returns NaN

If provided d2 <= 8, the function returns NaN.

var v = kurtosis( 1.0, 8.0 );
// returns NaN

v = kurtosis( 2.2, 5.5 );
// returns NaN

v = kurtosis( 3.0, -1.0 );
// returns NaN

Examples

import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@deno/mod.js';
import EPS from 'https://cdn.jsdelivr.net/gh/stdlib-js/constants-float64-eps@deno/mod.js';
import kurtosis from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-f-kurtosis@deno/mod.js';

var d1;
var d2;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    d1 = ( randu()*10.0 ) + EPS;
    d2 = ( randu()*20.0 ) + EPS;
    v = kurtosis( d1, d2 );
    console.log( 'd1: %d, d2: %d, Kurt(X;d1,d2): %d', d1.toFixed( 4 ), d2.toFixed( 4 ), v.toFixed( 4 ) );
}

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Notice

This package is part of stdlib, a standard library with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2025. The Stdlib Authors.