npm package: @stdlib/stats-base-dists-binomial-kurtosis
Description: Binomial 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] -->

> [Binomial][binomial-distribution] distribution [excess kurtosis][kurtosis].

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

The [excess kurtosis][kurtosis] for a [binomial][binomial-distribution] random variable is

<!-- <equation class="equation" label="eq:binomial_kurtosis" align="center" raw="\operatorname{Kurt}\left( X \right) = {\frac {1-6p(1-p)}{np(1-p)}}" alt="Excess kurtosis for a binomial distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{Kurt}\left( X \right) = {\frac {1-6p(1-p)}{np(1-p)}}" data-equation="eq:binomial_kurtosis">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/binomial/kurtosis/docs/img/equation_binomial_kurtosis.svg" alt="Excess kurtosis for a binomial distribution.">
    <br>
</div>

<!-- </equation> -->

where `n` is the number of trials and `p` is the success probability.

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### kurtosis( n, p )

Returns the [excess kurtosis][kurtosis] of a [binomial][binomial-distribution] distribution with number of trials `n` and success probability `p`.

```javascript
var v = kurtosis( 20, 0.1 );
// returns ~0.256

v = kurtosis( 50, 0.5 );
// returns ~-0.04
```

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

```javascript
var v = kurtosis( NaN, 0.5 );
// returns NaN

v = kurtosis( 20, NaN );
// returns NaN
```

If provided a number of trials `n` which is not a nonnegative integer, the function returns `NaN`.

```javascript
var v = kurtosis( 1.5, 0.5 );
// returns NaN

v = kurtosis( -2.0, 0.5 );
// returns NaN
```

If provided a success probability `p` outside of `[0,1]`, the function returns `NaN`.

```javascript
var v = kurtosis( 20, -1.0 );
// returns NaN

v = kurtosis( 20, 1.5 );
// 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 discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var kurtosis = require( '@stdlib/stats-base-dists-binomial-kurtosis' );

var opts = {
    'dtype': 'float64'
};
var n = discreteUniform( 10, 0, 100, opts );
var p = uniform( 10, 0.0, 1.0, opts );

logEachMap( 'n: %0.4f, p: %0.4f, Kurt(X;n,p): %0.4f', n, p, 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/binomial/kurtosis.h"
```

#### stdlib_base_dists_binomial_kurtosis( n, p )

Returns the [excess kurtosis][kurtosis] of a [binomial][binomial-distribution] distribution with number of trials `n` and success probability `p`.

```c
double out = stdlib_base_dists_binomial_kurtosis( 100, 0.1 );
// returns ~0.051
```

The function accepts the following arguments:

-   **n**: `[in] int32_t` number of trials.
-   **p**: `[in] double` success probability.

```c
double stdlib_base_dists_binomial_kurtosis( const int32_t n, const double p );
```

</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/binomial/kurtosis.h"
#include "stdlib/math/base/special/ceil.h"
#include <stdlib.h>
#include <stdint.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 ) {
    int32_t n;
    double p;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        n = stdlib_base_ceil( random_uniform( 0.0, 100.0 ) );
        p = random_uniform( 0.0, 1.0 );
        y = stdlib_base_dists_binomial_kurtosis( n, p );
        printf( "n: %d, p: %lf, Kurt(X;n,p): %lf\n", n, p, y );
    }

    return 0;
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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</section>

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<section class="related">

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

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