Kurtosis

Beta distribution excess kurtosis.

The excess kurtosis for a beta random variable is

where α > 0 is the first shape parameter and β > 0 is the second shape parameter.

Installation

npm install @stdlib/stats-base-dists-beta-kurtosis

Usage

var kurtosis = require( '@stdlib/stats-base-dists-beta-kurtosis' );

kurtosis( alpha, beta )

Returns the excess kurtosis of a beta distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var v = kurtosis( 1.0, 1.0 );
// returns -1.2

v = kurtosis( 4.0, 12.0 );
// returns ~0.082

v = kurtosis( 8.0, 2.0 );
// returns ~0.490

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

var v = kurtosis( NaN, 2.0 );
// returns NaN

v = kurtosis( 2.0, NaN );
// returns NaN

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

var v = kurtosis( 0.0, 1.0 );
// returns NaN

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

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

var v = kurtosis( 1.0, 0.0 );
// returns NaN

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

Examples

var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var kurtosis = require( '@stdlib/stats-base-dists-beta-kurtosis' );

var alpha;
var beta;
var v;
var i;

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

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, 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

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.