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

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# Kurtosis

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> [Geometric][geometric-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 [geometric][geometric-distribution] random variable is

<!-- <equation class="equation" label="eq:geometric_kurtosis" align="center" raw="\operatorname{Kurt}\left( X \right) = 6+{\frac{p^{2}}{1-p}}" alt="Excess kurtosis for a geometric distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{Kurt}\left( X \right) = 6+{\frac{p^{2}}{1-p}}" data-equation="eq:geometric_kurtosis">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/geometric/kurtosis/docs/img/equation_geometric_kurtosis.svg" alt="Excess kurtosis for a geometric distribution.">
    <br>
</div>

<!-- </equation> -->

where `p` is the success probability.

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### kurtosis( p )

Returns the [excess kurtosis][kurtosis] of a [geometric][geometric-distribution] distribution with success probability `p`.

```javascript
var v = kurtosis( 0.1 );
// returns ~6.011

v = kurtosis( 0.5 );
// returns 6.5
```

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

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

v = kurtosis( 1.5 );
// returns NaN

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-geometric-kurtosis' );

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

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

#### stdlib_base_dists_geometric_kurtosis( p )

Returns the [excess kurtosis][kurtosis] of a [geometric][geometric-distribution] distribution with success probability `p`.

```c
double out = stdlib_base_dists_geometric_kurtosis( 0.5 );
// returns 6.5
```

The function accepts the following arguments:

-   **p**: `[in] double` success probability.

```c
double stdlib_base_dists_geometric_kurtosis( const double p );
```

</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/geometric/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 p;
    double y;
    int i;

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

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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<section class="references">

</section>

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<section class="related">

</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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[geometric-distribution]: https://en.wikipedia.org/wiki/Geometric_distribution

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

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