@stdlib/stats/base/dists/rayleigh/kurtosis/README.md

Standard library statistical functions.

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# Kurtosis

> [Rayleigh][rayleigh-distribution] distribution [excess kurtosis][kurtosis].

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

<!-- <equation class="equation" label="eq:rayleigh_kurtosis" align="center" raw="\operatorname{Kurt}\left( X \right) = \sigma \sqrt{2 \ln(2)}" alt="Excess kurtosis for a Rayleigh distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{Kurt}\left( X \right) = \sigma \sqrt{2 \ln(2)}" data-equation="eq:rayleigh_kurtosis">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/rayleigh/kurtosis/docs/img/equation_rayleigh_kurtosis.svg" alt="Excess kurtosis for a Rayleigh distribution.">
    <br>
</div>

<!-- </equation> -->

where `σ > 0` is the scale parameter.

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## Usage

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

#### kurtosis( sigma )

Returns the [excess kurtosis][kurtosis] of a [Rayleigh][rayleigh-distribution] distribution with scale parameter `sigma`.

```javascript
var y = kurtosis( 9.0 );
// returns ~0.245

y = kurtosis( 4.5 );
// returns ~0.245
```

If provided `sigma < 0`, the function returns `NaN`.

```javascript
var y = kurtosis( -1.0 );
// returns NaN
```

</section>

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## Examples

<!-- eslint no-undef: "error" -->

```javascript
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var kurtosis = require( '@stdlib/stats/base/dists/rayleigh/kurtosis' );

var sigma;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    sigma = randu() * 20.0;
    y = kurtosis( sigma );
    console.log( 'σ: %d, Kurt(X,σ): %d', sigma.toFixed( 4 ), y.toFixed( 4 ) );
}
```

</section>

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</section>

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[rayleigh-distribution]: https://en.wikipedia.org/wiki/Rayleigh_distribution

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

</section>

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