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

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# Kurtosis

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> [Exponential][exponential-distribution] distribution [excess kurtosis][kurtosis].

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<section class="intro">

The [excess kurtosis][kurtosis] for an [exponential][exponential-distribution] random variable with rate parameter `λ` is

<!-- <equation class="equation" label="eq:exponential_kurtosis" align="center" raw="\operatorname{Kurt}\left( X \right) = 6" alt="Excess kurtosis for an exponential distribution."> -->

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

<!-- </equation> -->

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### kurtosis( lambda )

Returns the [excess kurtosis][kurtosis] of an [exponential][exponential-distribution] distribution with rate parameter `lambda`.

```javascript
var v = kurtosis( 9.0 );
// returns 6.0

v = kurtosis( 0.5 );
// returns 6.0
```

If provided `lambda < 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-exponential-kurtosis' );

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

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

</section>

<!-- /.examples -->

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* * *

<section class="c">

## C APIs

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<section class="intro">

</section>

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<section class="usage">

### Usage

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

#### stdlib_base_dists_exponential_kurtosis( lambda )

Returns the excess kurtosis of an exponential distribution.

```c
double out = stdlib_base_dists_exponential_kurtosis( 9.0 );
// returns 6.0
```

The function accepts the following arguments:

-   **lambda**: `[in] double` rate parameter.

```c
double stdlib_base_dists_exponential_kurtosis( const double lambda );
```

</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/exponential/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 lambda;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        lambda = random_uniform( 0.0, 20.0 );
        y = stdlib_base_dists_exponential_kurtosis( lambda );
        printf( "λ: %lf, Kurt(X;λ): %lf\n", lambda, y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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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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[exponential-distribution]: https://en.wikipedia.org/wiki/Exponential_distribution

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

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