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# Median

> [Cauchy][cauchy-distribution] distribution [median][median].

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The [median][median] for a [Cauchy][cauchy-distribution] random variable with location parameter `x0` and scale parameter `Ɣ > 0` is

<!-- <equation class="equation" label="eq:cauchy_median" align="center" raw="\operatorname{Median}\left( X \right) = x_0" alt="Median for a Cauchy distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{Median}\left( X \right) = x_0" data-equation="eq:cauchy_median">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/7e0a95722efd9c771b129597380c63dc6715508b/lib/node_modules/@stdlib/stats/base/dists/cauchy/median/docs/img/equation_cauchy_median.svg" alt="Median for a Cauchy distribution.">
    <br>
</div>

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</section>

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<section class="usage">

## Usage

```javascript
var median = require( '@stdlib/stats/base/dists/cauchy/median' );
```

#### median( x0, gamma )

Returns the [median][median] of a [Cauchy][cauchy-distribution] distribution with location parameter `x0` and scale parameter `gamma`.

```javascript
var v = median( 10.0, 5.0 );
// returns 10.0

v = median( 7.0, 2.0 );
// returns 7.0
```

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

```javascript
var v = median( NaN, 5.0 );
// returns NaN

v = median( 20.0, NaN );
// returns NaN
```

If provided `gamma <= 0`, the function returns `NaN`.

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

v = median( 1.0, 0.0 );
// 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 EPS = require( '@stdlib/constants/float64/eps' );
var median = require( '@stdlib/stats/base/dists/cauchy/median' );

var gamma;
var x0;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    x0 = randu() * 100.0;
    gamma = ( randu()*10.0 ) + EPS;
    v = median( x0, gamma );
    console.log( 'x0: %d, γ: %d, Median(X;x0,γ): %d', x0.toFixed( 4 ), gamma.toFixed( 4 ), v.toFixed( 4 ) );
}
```

</section>

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</section>

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<section class="links">

[cauchy-distribution]: https://en.wikipedia.org/wiki/Cauchy_distribution

[median]: https://en.wikipedia.org/wiki/Median

</section>

<!-- /.links -->
