@stdlib/stats/base/dists/laplace/pdf/README.md

Standard library statistical functions.

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# Probability Density Function

> [Laplace][laplace-distribution] distribution probability density function (PDF).

<section class="intro">

The [probability density function][pdf] (PDF) for a [Laplace][laplace-distribution] random variable is

<!-- <equation class="equation" label="eq:laplace_pdf" align="center" raw="f(x\mid\mu,b) = \frac{1}{2b} \exp \left( -\frac{|x-\mu|}{b} \right)" alt="Probability density function (PDF) for a Laplace distribution."> -->

<div class="equation" align="center" data-raw-text="f(x\mid\mu,b) = \frac{1}{2b} \exp \left( -\frac{|x-\mu|}{b} \right)" data-equation="eq:laplace_pdf">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/laplace/pdf/docs/img/equation_laplace_pdf.svg" alt="Probability density function (PDF) for a Laplace distribution.">
    <br>
</div>

<!-- </equation> -->

where `mu` is the location parameter and `b > 0` is the scale parameter (also called diversity).

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var pdf = require( '@stdlib/stats/base/dists/laplace/pdf' );
```

#### pdf( x, mu, b )

Evaluates the [probability density function][pdf] (PDF) for a [Laplace][laplace-distribution] distribution with parameters `mu` (location parameter) and `b > 0` (scale parameter).

```javascript
var y = pdf( 2.0, 0.0, 1.0 );
// returns ~0.068

y = pdf( -1.0, 2.0, 3.0 );
// returns ~0.061

y = pdf( 2.5, 2.0, 3.0 );
// returns ~0.141
```

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

```javascript
var y = pdf( NaN, 0.0, 1.0 );
// returns NaN

y = pdf( 0.0, NaN, 1.0 );
// returns NaN

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

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

```javascript
var y = pdf( 2.0, 0.0, -1.0 );
// returns NaN

y = pdf( 2.0, 8.0, 0.0 );
// returns NaN
```

#### pdf.factory( mu, b )

Returns a `function` for evaluating the [PDF][pdf] of a [Laplace][laplace-distribution] distribution with parameters `mu` (location parameter) and `b > 0` (scale parameter).

```javascript
var mypdf = pdf.factory( 10.0, 2.0 );

var y = mypdf( 10.0 );
// returns 0.25

y = mypdf( 5.0 );
// returns ~0.021

y = mypdf( 12.0 );
// returns ~0.092
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

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

var mu;
var b;
var x;
var y;
var i;

for ( i = 0; i < 100; i++ ) {
    x = randu() * 10.0;
    mu = randu() * 10.0;
    b = randu() * 10.0;
    y = pdf( x, mu, b );
    console.log( 'x: %d, µ: %d, b: %d, f(x;µ,b): %d', x.toFixed( 4 ), mu.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
}
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

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<section class="links">

[laplace-distribution]: https://en.wikipedia.org/wiki/Laplace_distribution

[pdf]: https://en.wikipedia.org/wiki/Probability_density_function

</section>

<!-- /.links -->