Kurtosis

Kumaraswamy's double bounded distribution excess kurtosis.

The excess kurtosis for a Kumaraswamy's double bounded random variable with first shape parameter a and second shape parameter b is

where the raw moments of the distribution are given by

with B denoting the beta function.

Installation

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

Usage

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

kurtosis( a, b )

Returns the excess kurtosis of a Kumaraswamy's double bounded distribution with first shape parameter a and second shape parameter b.

var v = kurtosis( 1.0, 1.0 );
// returns ~1.8

v = kurtosis( 4.0, 12.0 );
// returns ~2.704

v = kurtosis( 2.0, 8.0 );
// returns ~2.666

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 a <= 0, the function returns NaN.

var y = kurtosis( -1.0, 0.5 );
// returns NaN

y = kurtosis( 0.0, 0.5 );
// returns NaN

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

var y = kurtosis( 0.5, -1.0 );
// returns NaN

y = kurtosis( 0.5, 0.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random-base-randu' );
var kurtosis = require( '@stdlib/stats-base-dists-kumaraswamy-kurtosis' );

var a;
var b;
var v;
var i;

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

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