Kurtosis

Inverse gamma distribution excess kurtosis.

The excess kurtosis for an inverse gamma random variable with shape parameter α and rate parameter β is

when α > 4. Otherwise, the kurtosis is not defined.

Installation

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

Usage

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

kurtosis( alpha, beta )

Returns the excess kurtosis of an inverse gamma distribution with parameters alpha (shape parameter) and beta (rate parameter).

var v = kurtosis( 7.0, 5.0 );
// returns 12.0

v = kurtosis( 6.0, 12.0 );
// returns 19.0

v = kurtosis( 8.0, 2.0 );
// returns ~8.7

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

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

v = kurtosis( 5.0, NaN );
// returns NaN

If provided alpha <= 4, the function returns NaN.

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

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

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

var v = kurtosis( 5.0, 0.0 );
// returns NaN

v = kurtosis( 5.0, -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-invgamma-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.