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https://github.com/stdlib-js/stats-base-dists-chisquare-kurtosis

Chi-squared distribution kurtosis.
https://github.com/stdlib-js/stats-base-dists-chisquare-kurtosis

chi-square chi-squared chisq chisquare chisquared continuous dist distribution excess javascript kurtosis node node-js nodejs statistics stats stdlib tails univariate

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Chi-squared distribution kurtosis.

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README 

        



  

    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][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] 



> [Chi-squared][chisquare-distribution] distribution [excess kurtosis][kurtosis].



The [excess kurtosis][kurtosis] for a [chi-squared][chisquare-distribution] random variable is



```math

\mathop{\mathrm{Kurt}}\left( X \right) = \frac{12}{k}

```



where `k > 0` is the degrees of freedom.



## Installation



```bash

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

```



Alternatively,



-   To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).

-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).

-   For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).



The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.



To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.



## Usage



```javascript

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

```



#### kurtosis( k )



Returns the [excess kurtosis][kurtosis] of a [chi-squared][chisquare-distribution] distribution with degrees of freedom `k`.



```javascript

var v = kurtosis( 9.0 );

// returns ~1.333



v = kurtosis( 0.5 );

// returns 24.0

```



If provided `k <= 0`, the function returns `NaN`.



```javascript

var v = kurtosis( -1.0 );

// returns NaN

```



## Examples



```javascript

var randu = require( '@stdlib/random-base-randu' );

var round = require( '@stdlib/math-base-special-round' );

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



var k;

var v;

var i;



for ( i = 0; i < 10; i++ ) {

    k = randu() * 20.0;

    v = kurtosis( k );

    console.log( 'k: %d, Kurt(X,k): %d', k.toFixed( 4 ), v.toFixed( 4 ) );

}

```



* * *



## Notice



This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].



#### Community



[![Chat][chat-image]][chat-url]



---



## License



See [LICENSE][stdlib-license].



## Copyright



Copyright © 2016-2024. The Stdlib [Authors][stdlib-authors].



[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-chisquare-kurtosis.svg

[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-chisquare-kurtosis



[test-image]: https://github.com/stdlib-js/stats-base-dists-chisquare-kurtosis/actions/workflows/test.yml/badge.svg?branch=main

[test-url]: https://github.com/stdlib-js/stats-base-dists-chisquare-kurtosis/actions/workflows/test.yml?query=branch:main



[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-chisquare-kurtosis/main.svg

[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-chisquare-kurtosis?branch=main



[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg

[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im



[stdlib]: https://github.com/stdlib-js/stdlib



[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors



[umd]: https://github.com/umdjs/umd

[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules



[deno-url]: https://github.com/stdlib-js/stats-base-dists-chisquare-kurtosis/tree/deno

[deno-readme]: https://github.com/stdlib-js/stats-base-dists-chisquare-kurtosis/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/stats-base-dists-chisquare-kurtosis/tree/umd

[umd-readme]: https://github.com/stdlib-js/stats-base-dists-chisquare-kurtosis/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/stats-base-dists-chisquare-kurtosis/tree/esm

[esm-readme]: https://github.com/stdlib-js/stats-base-dists-chisquare-kurtosis/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/stats-base-dists-chisquare-kurtosis/blob/main/branches.md



[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-chisquare-kurtosis/main/LICENSE



[chisquare-distribution]: https://en.wikipedia.org/wiki/Chi-squared_distribution



[kurtosis]: https://en.wikipedia.org/wiki/Kurtosis