npm package: @stdlib/stats-base-dists-laplace
Description: Laplace distribution.
Author: The Stdlib Authors
Latest version: 0.3.1

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# Laplace

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> Laplace distribution.

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-laplace
```

</section>

<section class="usage">

## Usage

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

#### laplace

Laplace distribution.

```javascript
var dist = laplace;
// returns {...}
```

The namespace contains the following distribution functions:

<!-- <toc pattern="*+(cdf|pdf|mgf|quantile)*"> -->

<div class="namespace-toc">

-   <span class="signature">[`cdf( x, mu, b )`][@stdlib/stats/base/dists/laplace/cdf]</span><span class="delimiter">: </span><span class="description">Laplace distribution cumulative distribution function.</span>
-   <span class="signature">[`logcdf( x, mu, b )`][@stdlib/stats/base/dists/laplace/logcdf]</span><span class="delimiter">: </span><span class="description">Laplace distribution logarithm of cumulative distribution function.</span>
-   <span class="signature">[`logpdf( x, mu, b )`][@stdlib/stats/base/dists/laplace/logpdf]</span><span class="delimiter">: </span><span class="description">Laplace distribution logarithm of probability density function (PDF).</span>
-   <span class="signature">[`mgf( t, mu, b )`][@stdlib/stats/base/dists/laplace/mgf]</span><span class="delimiter">: </span><span class="description">Laplace distribution moment-generating function (MGF).</span>
-   <span class="signature">[`pdf( x, mu, b )`][@stdlib/stats/base/dists/laplace/pdf]</span><span class="delimiter">: </span><span class="description">Laplace distribution probability density function (PDF).</span>
-   <span class="signature">[`quantile( p, mu, b )`][@stdlib/stats/base/dists/laplace/quantile]</span><span class="delimiter">: </span><span class="description">Laplace distribution quantile function.</span>

</div>

<!-- </toc> -->

The namespace contains the following functions for calculating distribution properties:

<!-- <toc pattern="*+(entropy|kurtosis|mean|median|mode|skewness|stdev|variance)*"> -->

<div class="namespace-toc">

-   <span class="signature">[`entropy( mu, b )`][@stdlib/stats/base/dists/laplace/entropy]</span><span class="delimiter">: </span><span class="description">Laplace distribution differential entropy.</span>
-   <span class="signature">[`kurtosis( mu, b )`][@stdlib/stats/base/dists/laplace/kurtosis]</span><span class="delimiter">: </span><span class="description">Laplace distribution excess kurtosis.</span>
-   <span class="signature">[`mean( mu, b )`][@stdlib/stats/base/dists/laplace/mean]</span><span class="delimiter">: </span><span class="description">Laplace distribution expected value.</span>
-   <span class="signature">[`median( mu, b )`][@stdlib/stats/base/dists/laplace/median]</span><span class="delimiter">: </span><span class="description">Laplace distribution median.</span>
-   <span class="signature">[`mode( mu, b )`][@stdlib/stats/base/dists/laplace/mode]</span><span class="delimiter">: </span><span class="description">Laplace distribution mode.</span>
-   <span class="signature">[`skewness( mu, b )`][@stdlib/stats/base/dists/laplace/skewness]</span><span class="delimiter">: </span><span class="description">Laplace distribution skewness.</span>
-   <span class="signature">[`stdev( mu, b )`][@stdlib/stats/base/dists/laplace/stdev]</span><span class="delimiter">: </span><span class="description">Laplace distribution standard deviation.</span>
-   <span class="signature">[`variance( mu, b )`][@stdlib/stats/base/dists/laplace/variance]</span><span class="delimiter">: </span><span class="description">Laplace distribution variance.</span>

</div>

<!-- </toc> -->

The namespace contains a constructor function for creating a [Laplace][laplace-distribution] distribution object.

<!-- <toc pattern="*ctor*"> -->

<div class="namespace-toc">

-   <span class="signature">[`Laplace( [mu, b] )`][@stdlib/stats/base/dists/laplace/ctor]</span><span class="delimiter">: </span><span class="description">Laplace distribution constructor.</span>

</div>

<!-- </toc> -->

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

var dist = new Laplace( 2.0, 4.0 );

var y = dist.cdf( 0.5 );
// returns ~0.344
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- TODO: better examples -->

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

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

var dist = new laplace.Laplace( 4.0, 2.0 );

console.log( dist.mu );
// => 4.0

console.log( dist.b );
// => 2.0

dist.mu = 6.0;
dist.b = 3.0;

console.log( dist.mu );
// => 6.0

console.log( dist.b );
// => 3.0

console.log( dist.kurtosis );
// => 3.0

console.log( dist.median );
// => 6.0

console.log( dist.variance );
// => 18.0

var mu = 4.0;
var b = 2.0;

console.log( laplace.pdf( 2.0, mu, b ) );
// => ~0.092

console.log( laplace.cdf( 2.0, mu, b ) );
// => ~0.184

console.log( laplace.quantile( 0.5, mu, b ) );
// => 4.0

mu = 6.0;
b = 3.0;

console.log( laplace.entropy( mu, b ) );
// => ~ 2.7918

console.log( laplace.mean( mu, b ) );
// => 6.0

console.log( laplace.median( mu, b ) );
// => 6.0

console.log( laplace.mode( mu, b ) );
// => 6.0

console.log( laplace.variance( mu, b ) );
// => 18.0

console.log( laplace.skewness( mu, b ) );
// => 0.0

var myquantile = laplace.quantile.factory( 10.0, 2.0 );

console.log( myquantile( 0.2 ) );
// => ~8.167

console.log( myquantile( 0.8 ) );
// => ~11.833

var mylogpdf = laplace.logpdf.factory( 10.0, 2.0 );

console.log( mylogpdf( 10.0) );
// => ~-1.386

console.log( mylogpdf( 5.0 ) );
// => ~-3.886
```

</section>

<!-- /.examples -->

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

<section class="related">

</section>

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