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

Standard library statistical functions.

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# Kurtosis

> [Binomial][binomial-distribution] distribution [excess kurtosis][kurtosis].

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

<!-- <equation class="equation" label="eq:binomial_kurtosis" align="center" raw="\operatorname{Kurt}\left( X \right) = {\frac {1-6p(1-p)}{np(1-p)}}" alt="Excess kurtosis for a binomial distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{Kurt}\left( X \right) = {\frac {1-6p(1-p)}{np(1-p)}}" data-equation="eq:binomial_kurtosis">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/binomial/kurtosis/docs/img/equation_binomial_kurtosis.svg" alt="Excess kurtosis for a binomial distribution.">
    <br>
</div>

<!-- </equation> -->

where `n` is the number of trials and `p` is the success probability.

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## Usage

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

#### kurtosis( n, p )

Returns the [excess kurtosis][kurtosis] of a [binomial][binomial-distribution] distribution with number of trials `n` and success probability `p`.

```javascript
var v = kurtosis( 20, 0.1 );
// returns ~0.256

v = kurtosis( 50, 0.5 );
// returns ~-0.04
```

If provided `NaN` as any argument, the function returns `NaN`.

```javascript
var v = kurtosis( NaN, 0.5 );
// returns NaN

v = kurtosis( 20, NaN );
// returns NaN
```

If provided a number of trials `n` which is not a nonnegative integer, the function returns `NaN`.

```javascript
var v = kurtosis( 1.5, 0.5 );
// returns NaN

v = kurtosis( -2.0, 0.5 );
// returns NaN
```

If provided a success probability `p` outside of `[0,1]`, the function returns `NaN`.

```javascript
var v = kurtosis( 20, -1.0 );
// returns NaN

v = kurtosis( 20, 1.5 );
// returns NaN
```

</section>

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</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/binomial/kurtosis' );

var v;
var i;
var n;
var p;

for ( i = 0; i < 10; i++ ) {
    n = round( randu() * 100.0 );
    p = randu();
    v = kurtosis( n, p );
    console.log( 'n: %d, p: %d, Kurt(X;n,p): %d', n, p.toFixed( 4 ), v.toFixed( 4 ) );
}
```

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</section>

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</section>

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[binomial-distribution]: https://en.wikipedia.org/wiki/Binomial_distribution

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

</section>

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