npm package: @stdlib/stats-base-dists-normal-kurtosis
Description: Normal distribution excess kurtosis.
Author: The Stdlib Authors
Latest version: 0.3.1

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# Kurtosis

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

> [Normal][normal-distribution] distribution [excess kurtosis][kurtosis].

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<section class="intro">

The [excess kurtosis][kurtosis] for a [normal][normal-distribution] random variable with mean `μ` and standard deviation `σ > 0` is

<!-- <equation class="equation" label="eq:normal_kurtosis" align="center" raw="\operatorname{Kurt}\left( X \right) = 0" alt="Excess kurtosis for a normal distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{Kurt}\left( X \right) = 0" data-equation="eq:normal_kurtosis">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/normal/kurtosis/docs/img/equation_normal_kurtosis.svg" alt="Excess kurtosis for a normal distribution.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

```javascript
var kurtosis = require( '@stdlib/stats-base-dists-normal-kurtosis' );
```

#### kurtosis( mu, sigma )

Returns the [excess kurtosis][kurtosis] for a [normal][normal-distribution] distribution with parameters `mu` (mean) and `sigma` (standard deviation).

```javascript
var y = kurtosis( 2.0, 1.0 );
// returns 0.0

y = kurtosis( -1.0, 4.0 );
// returns 0.0
```

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

```javascript
var y = kurtosis( NaN, 1.0 );
// returns NaN

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

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

```javascript
var y = kurtosis( 0.0, 0.0 );
// returns NaN

y = kurtosis( 0.0, -1.0 );
// returns NaN
```

</section>

<!-- /.usage -->

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<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-normal-kurtosis' );

var opts = {
    'dtype': 'float64'
};
var sigma = uniform( 10, 0.0, 20.0, opts );
var mu = uniform( 10, -5.0, 5.0, opts );

logEachMap( 'µ: %0.4f, σ: %0.4f, Kurt(X;µ,σ): %0.4f', mu, sigma, 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/normal/kurtosis.h"
```

#### stdlib_base_dists_normal_kurtosis( mu, sigma )

Returns the [excess kurtosis][kurtosis] for a [normal][normal-distribution] distribution with parameters `mu` (mean) and `sigma` (standard deviation).

```c
double out = stdlib_base_dists_normal_kurtosis( 0.0, 1.0 );
// returns 0.0
```

The function accepts the following arguments:

-   **mu**: `[in] double` mean.
-   **sigma**: `[in] double` standard deviation.

```c
double stdlib_base_dists_normal_kurtosis( const double mu, const double sigma );
```

</section>

<!-- /.usage -->

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<section class="notes">

</section>

<!-- /.notes -->

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

<section class="examples">

### Examples

```c
#include "stdlib/stats/base/dists/normal/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 sigma;
    double mu;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        mu = random_uniform( -5.0, 5.0 );
        sigma = random_uniform( 0.0, 20.0 );
        y = stdlib_base_dists_normal_kurtosis( mu, sigma );
        printf( "µ: %.4f, σ: %.4f, Kurt(X;µ,σ): %.4f\n", mu, sigma, y );
    }
}
```

</section>

<!-- /.examples -->

</section>

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* * *

## 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].

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---

## License

See [LICENSE][stdlib-license].


## Copyright

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

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[normal-distribution]: https://en.wikipedia.org/wiki/Normal_distribution

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

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