@stdlib/stats-base-dists-normal-kurtosis/README.md

Normal distribution excess kurtosis.

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# Kurtosis

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> [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>

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<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>

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<section class="notes">

</section>

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<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>

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* * *

<section class="c">

## C APIs

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</section>

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<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>

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<section class="notes">

</section>

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<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>

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</section>

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## License

See [LICENSE][stdlib-license].


## Copyright

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

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

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