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# Kurtosis

> [Poisson][poisson-distribution] distribution [excess kurtosis][kurtosis].

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<section class="intro">

The [excess kurtosis][kurtosis] for a [Poisson][poisson-distribution] random variable is

<!-- <equation class="equation" label="eq:poisson_kurtosis" align="center" raw="\operatorname{Kurt}\left( X \right) = \lambda^{-1}" alt="Excess kurtosis for a Poisson distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{Kurt}\left( X \right) = \lambda^{-1}" data-equation="eq:poisson_kurtosis">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/7e0a95722efd9c771b129597380c63dc6715508b/lib/node_modules/@stdlib/stats/base/dists/poisson/kurtosis/docs/img/equation_poisson_kurtosis.svg" alt="Excess kurtosis for a Poisson distribution.">
    <br>
</div>

<!-- </equation> -->

where `λ` is the mean parameter.

</section>

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<section class="usage">

## Usage

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

#### kurtosis( lambda )

Returns the [excess kurtosis][kurtosis] of a [Poisson][poisson-distribution] distribution with mean parameter `lambda`.

```javascript
var v = kurtosis( 9.0 );
// returns ~0.111

v = kurtosis( 0.5 );
// returns 2.0
```

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>

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<section class="examples">

## 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/poisson/kurtosis' );

var lambda;
var v;
var i;

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

</section>

<!-- /.examples -->

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<section class="references">

</section>

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<section class="links">

[poisson-distribution]: https://en.wikipedia.org/wiki/Poisson_distribution

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

</section>

<!-- /.links -->
