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

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# Gumbel

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

> Gumbel distribution constructor.

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<section class="intro">

</section>

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<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### Gumbel( \[mu, beta] )

Returns a [Gumbel][gumbel-distribution] distribution object.

```javascript
var gumbel = new Gumbel();

var mean = gumbel.mean;
// returns ~0.577
```

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

```javascript
var gumbel = new Gumbel( 2.0, 4.0 );

var mean = gumbel.mean;
// returns ~4.309
```

* * *

## gumbel

A [Gumbel][gumbel-distribution] distribution object has the following properties and methods...

### Writable Properties

#### gumbel.mu

Location parameter of the distribution.

```javascript
var gumbel = new Gumbel();

var mu = gumbel.mu;
// returns 0.0

gumbel.mu = 3.0;

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

#### gumbel.beta

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

```javascript
var gumbel = new Gumbel( 2.0, 4.0 );

var beta = gumbel.beta;
// returns 4.0

gumbel.beta = 3.0;

beta = gumbel.beta;
// returns 3.0
```

* * *

### Computed Properties

#### Gumbel.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var gumbel = new Gumbel( 4.0, 12.0 );

var entropy = gumbel.entropy;
// returns ~4.062
```

#### Gumbel.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var gumbel = new Gumbel( 4.0, 12.0 );

var kurtosis = gumbel.kurtosis;
// returns 2.4
```

#### Gumbel.prototype.mean

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

```javascript
var gumbel = new Gumbel( 4.0, 12.0 );

var mu = gumbel.mean;
// returns ~10.927
```

#### Gumbel.prototype.median

Returns the [median][median].

```javascript
var gumbel = new Gumbel( 4.0, 12.0 );

var median = gumbel.median;
// returns ~8.398
```

#### Gumbel.prototype.mode

Returns the [mode][mode].

```javascript
var gumbel = new Gumbel( 4.0, 12.0 );

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

#### Gumbel.prototype.skewness

Returns the [skewness][skewness].

```javascript
var gumbel = new Gumbel( 4.0, 12.0 );

var skewness = gumbel.skewness;
// returns ~1.14
```

#### Gumbel.prototype.stdev

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

```javascript
var gumbel = new Gumbel( 4.0, 12.0 );

var s = gumbel.stdev;
// returns ~15.391
```

#### Gumbel.prototype.variance

Returns the [variance][variance].

```javascript
var gumbel = new Gumbel( 4.0, 12.0 );

var s2 = gumbel.variance;
// returns ~236.871
```

* * *

### Methods

#### Gumbel.prototype.cdf( x )

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

```javascript
var gumbel = new Gumbel( 2.0, 4.0 );

var y = gumbel.cdf( 0.5 );
// returns ~0.233
```

#### Gumbel.prototype.logcdf( x )

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

```javascript
var gumbel = new Gumbel( 2.0, 4.0 );

var y = gumbel.logcdf( 2.0 );
// returns -1.0
```

#### Gumbel.prototype.logpdf( x )

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

```javascript
var gumbel = new Gumbel( 2.0, 4.0 );

var y = gumbel.logpdf( 0.8 );
// returns ~-2.436
```

#### Gumbel.prototype.mgf( t )

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

```javascript
var gumbel = new Gumbel( 2.0, 4.0 );

var y = gumbel.mgf( 0.1 );
// returns ~1.819
```

#### Gumbel.prototype.pdf( x )

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

```javascript
var gumbel = new Gumbel( 2.0, 4.0 );

var y = gumbel.pdf( 2.0 );
// returns ~0.092
```

#### Gumbel.prototype.quantile( p )

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

```javascript
var gumbel = new Gumbel( 2.0, 4.0 );

var y = gumbel.quantile( 0.5 );
// returns ~3.466

y = gumbel.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 Gumbel = require( '@stdlib/stats-base-dists-gumbel-ctor' );

var gumbel = new Gumbel( 2.0, 4.0 );

var mean = gumbel.mean;
// returns ~4.309

var median = gumbel.median;
// returns ~3.466

var s2 = gumbel.variance;
// returns ~26.319

var y = gumbel.cdf( 0.8 );
// returns ~0.259
```

</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].

</section>

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

[gumbel-distribution]: https://en.wikipedia.org/wiki/Gumbel_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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