npm package: @stdlib/stats-base-dists-planck-kurtosis
Description: Planck (discrete exponential) distribution excess kurtosis.
Author: The Stdlib Authors
Latest version: 0.1.1

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# Kurtosis

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> Planck (discrete exponential) distribution [excess kurtosis][kurtosis].

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<section class="intro">

The [excess kurtosis][kurtosis] for a Planck random variable is

<!-- <equation class="equation" label="eq:planck_kurtosis" align="center" raw="\mathop{\mathrm{Kurt}}\left( X \right) = 4 + 2 \cosh(\lambda)" alt="Excess kurtosis for a Planck distribution."> -->

<!-- </equation> -->

where `λ` is the shape parameter.

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### kurtosis( lambda )

Returns the [excess kurtosis][kurtosis] of a Planck distribution with shape parameter `lambda`.

```javascript
var v = kurtosis( 0.1 );
// returns ~6.0100

v = kurtosis( 1.5 );
// returns ~8.7048
```

If provided a shape parameter `lambda` which is nonpositive or `NaN`, the function returns `NaN`.

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

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

var opts = {
    'dtype': 'float64'
};
var lambda = uniform( 10, 0.1, 10.0, opts );

logEachMap( 'λ: %0.4f, Kurt(X;λ): %0.4f', lambda, 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/planck/kurtosis.h"
```

#### stdlib_base_dists_planck_kurtosis( lambda )

Returns the [excess kurtosis][kurtosis] of a Planck distribution with shape parameter `lambda`.

```c
double out = stdlib_base_dists_planck_kurtosis( 0.1 );
// returns ~6.0100
```

The function accepts the following arguments:

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

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

</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/planck/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( 0.1, 5.0 );
        y = stdlib_base_dists_planck_kurtosis( lambda );
        printf( "λ: %lf, Kurt(X;λ): %lf\n", lambda, 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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<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].

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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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