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About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

Kurtosis

NPM version Build Status Coverage Status

Inverse gamma distribution excess kurtosis.

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

$$\mathop{\mathrm{Kurt}}\left( X \right) = \frac {30\,\alpha -66}{(\alpha -3)(\alpha -4)}$$

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

Usage

import kurtosis from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-invgamma-kurtosis@esm/index.mjs';

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

<!DOCTYPE html>
<html lang="en">
<body>
<script type="module">

import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@esm/index.mjs';
import EPS from 'https://cdn.jsdelivr.net/gh/stdlib-js/constants-float64-eps@esm/index.mjs';
import kurtosis from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-invgamma-kurtosis@esm/index.mjs';

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 ) );
}

</script>
</body>
</html>

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.

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.