npm package: @stdlib/stats-base-dists-laplace-ctor
Description: Laplace distribution constructor.
Author: The Stdlib Authors
Latest version: 0.2.3

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# Laplace

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Laplace distribution constructor.

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### Laplace( \[mu, b] )

Returns a [Laplace][laplace-distribution] distribution object.

```javascript
var laplace = new Laplace();

var mu = laplace.mean;
// returns 0.0
```

By default, `mu = 0.0` and `b = 1.0`. To create a distribution having a different `mu` (location parameter) and `b` (scale parameter), provide the corresponding arguments.

```javascript
var laplace = new Laplace( 2.0, 4.0 );

var mu = laplace.mean;
// returns 2.0
```

* * *

## laplace

A [Laplace][laplace-distribution] distribution object has the following properties and methods...

### Writable Properties

#### laplace.mu

Location parameter of the distribution.

```javascript
var laplace = new Laplace();

var mu = laplace.mu;
// returns 0.0

laplace.mu = 3.0;

mu = laplace.mu;
// returns 3.0
```

#### laplace.b

Scale parameter of the distribution. `b` **must** be a positive number.

```javascript
var laplace = new Laplace( 2.0, 4.0 );

var b = laplace.b;
// returns 4.0

laplace.b = 3.0;

b = laplace.b;
// returns 3.0
```

* * *

### Computed Properties

#### Laplace.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var laplace = new Laplace( 4.0, 12.0 );

var entropy = laplace.entropy;
// returns ~4.178
```

#### Laplace.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var laplace = new Laplace( 4.0, 12.0 );

var kurtosis = laplace.kurtosis;
// returns 3.0
```

#### Laplace.prototype.mean

Returns the [expected value][expected-value].

```javascript
var laplace = new Laplace( 4.0, 12.0 );

var mu = laplace.mean;
// returns 4.0
```

#### Laplace.prototype.median

Returns the [median][median].

```javascript
var laplace = new Laplace( 4.0, 12.0 );

var median = laplace.median;
// returns 4.0
```

#### Laplace.prototype.mode

Returns the [mode][mode].

```javascript
var laplace = new Laplace( 4.0, 12.0 );

var mode = laplace.mode;
// returns 4.0
```

#### Laplace.prototype.skewness

Returns the [skewness][skewness].

```javascript
var laplace = new Laplace( 4.0, 12.0 );

var skewness = laplace.skewness;
// returns 0.0
```

#### Laplace.prototype.stdev

Returns the [standard deviation][standard-deviation].

```javascript
var laplace = new Laplace( 4.0, 12.0 );

var s = laplace.stdev;
// returns ~16.971
```

#### Laplace.prototype.variance

Returns the [variance][variance].

```javascript
var laplace = new Laplace( 4.0, 12.0 );

var s2 = laplace.variance;
// returns 288.0
```

* * *

### Methods

#### Laplace.prototype.cdf( x )

Evaluates the [cumulative distribution function][cdf] (CDF).

```javascript
var laplace = new Laplace( 2.0, 4.0 );

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

#### Laplace.prototype.logcdf( x )

Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF).

```javascript
var laplace = new Laplace( 2.0, 4.0 );

var y = laplace.logcdf( 2.0 );
// returns ~-0.693
```

#### Laplace.prototype.logpdf( x )

Evaluates the natural logarithm of the [probability density function][pdf] (PDF).

```javascript
var laplace = new Laplace( 2.0, 4.0 );

var y = laplace.logpdf( 0.8 );
// returns ~-2.379
```

#### Laplace.prototype.mgf( t )

Evaluates the [moment-generating function][mgf] (MGF).

```javascript
var laplace = new Laplace( 2.0, 4.0 );

var y = laplace.mgf( 0.2 );
// returns ~4.144
```

#### Laplace.prototype.pdf( x )

Evaluates the [probability density function][pdf] (PDF).

```javascript
var laplace = new Laplace( 2.0, 4.0 );

var y = laplace.pdf( 2.0 );
// returns 0.125
```

#### Laplace.prototype.quantile( p )

Evaluates the [quantile function][quantile-function] at probability `p`.

```javascript
var laplace = new Laplace( 2.0, 4.0 );

var y = laplace.quantile( 0.5 );
// returns 2.0

y = laplace.quantile( 1.9 );
// returns NaN
```

</section>

<!-- /.usage -->

<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- Package usage examples. -->

* * *

<section class="examples">

## Examples

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

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

var laplace = new Laplace( 2.0, 4.0 );

var mean = laplace.mean;
// returns 2.0

var median = laplace.median;
// returns 2.0

var s2 = laplace.variance;
// returns 32.0

var y = laplace.cdf( 0.8 );
// returns ~0.37
```

</section>

<!-- /.examples -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-laplace-ctor/main/LICENSE

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

[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function

[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function

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

[quantile-function]: https://en.wikipedia.org/wiki/Quantile_function

[entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29

[expected-value]: https://en.wikipedia.org/wiki/Expected_value

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

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

[mode]: https://en.wikipedia.org/wiki/Mode_%28statistics%29

[skewness]: https://en.wikipedia.org/wiki/Skewness

[standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation

[variance]: https://en.wikipedia.org/wiki/Variance

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