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# Median

> [Lognormal][lognormal-distribution] distribution [median][median].

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<section class="intro">

The [median][median] for a [lognormal][lognormal-distribution] random variable with location parameter `μ` and scale parameter `σ > 0` is

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

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

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According to the definition, the _natural logarithm_ of a random variable from a
[lognormal distribution][lognormal-distribution] follows a [normal distribution][normal-distribution].

</section>

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<section class="usage">

## Usage

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

#### median( mu, sigma )

Returns the [median][median] for a [lognormal][lognormal-distribution] distribution with location `mu` and scale `sigma`.

```javascript
var y = median( 2.0, 1.0 );
// returns ~7.389

y = median( 0.0, 1.0 );
// returns 1.0

y = median( -1.0, 4.0 );
// returns ~0.368
```

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

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

y = median( 0.0, NaN );
// returns NaN
```

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

```javascript
var y = median( 0.0, 0.0 );
// returns NaN

y = median( 0.0, -1.0 );
// returns NaN
```

</section>

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</section>

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<section class="examples">

## Examples

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

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

var sigma;
var mu;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    mu = ( randu()*10.0 ) - 5.0;
    sigma = randu() * 20.0;
    y = median( mu, sigma );
    console.log( 'µ: %d, σ: %d, Median(X;µ,σ): %d', mu.toFixed( 4 ), sigma.toFixed( 4 ), y.toFixed( 4 ) );
}
```

</section>

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</section>

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<section class="links">

[lognormal-distribution]: https://en.wikipedia.org/wiki/Log-normal_distribution

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

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

</section>

<!-- /.links -->
