npm package: @stdlib/stats-base-dists-chisquare-kurtosis
Description: Chi-squared distribution kurtosis.
Author: The Stdlib Authors
Latest version: 0.3.1

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</details>

# Kurtosis

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

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

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<section class="intro">

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

<!-- <equation class="equation" label="eq:chisquare_kurtosis" align="center" raw="\operatorname{Kurt}\left( X \right) = \frac{12}{k}" alt="Excess kurtosis for a chi-squared distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{Kurt}\left( X \right) = \frac{12}{k}" data-equation="eq:chisquare_kurtosis">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/chisquare/kurtosis/docs/img/equation_chisquare_kurtosis.svg" alt="Excess kurtosis for a chi-squared distribution.">
    <br>
</div>

<!-- </equation> -->

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

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## 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
```

</section>

<!-- /.usage -->

<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- Package usage examples. -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var kurtosis = require( '@stdlib/stats-base-dists-chisquare-kurtosis' );

var opts = {
    'dtype': 'float64'
};
var k = uniform( 10, 0.0, 20.0, opts );

logEachMap( 'k: %0.4f, Kurt(X;k): %0.4f', k, kurtosis );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

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<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/stats/base/dists/chisquare/kurtosis.h"
```

#### stdlib_base_dists_chisquare_kurtosis( k )

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

```c
double out = stdlib_base_dists_chisquare_kurtosis( 9.0 );
// returns ~1.333
```

The function accepts the following arguments:

-   **k**: `[in] double` degrees of freedom (must be positive).

```c
double stdlib_base_dists_chisquare_kurtosis( const double k );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/stats/base/dists/chisquare/kurtosis.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v * ( max - min ) );
}

int main( void ) {
    double result;
    double k;
    int i;

    for ( i = 0; i < 10; i++ ) {
        k = random_uniform( 1.0, 10.0 );
        result = stdlib_base_dists_chisquare_kurtosis( k );
        printf( "k: %lf, Kurt(X,k): %lf \n", k, result );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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<section class="references">

</section>

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<section class="related">

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<section class="main-repo" >

* * *

## 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

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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

</section>

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