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

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# Erlang

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> Erlang 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-erlang-ctor
```

</section>

<section class="usage">

## Usage

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

#### Erlang( \[k, lambda] )

Returns an [Erlang][erlang-distribution] distribution object.

```javascript
var erlang = new Erlang();

var mode = erlang.mode;
// returns 0.0
```

By default, `k = 1.0` and `lambda = 1.0`. To create a distribution having a different `k` (shape parameter) and `lambda` (rate parameter), provide the corresponding arguments.

```javascript
var erlang = new Erlang( 2, 4.0 );

var mode = erlang.mode;
// returns 0.25
```

* * *

## erlang

An [Erlang][erlang-distribution] distribution object has the following properties and methods...

### Writable Properties

#### erlang.k

Shape parameter of the distribution. `k` **must** be a positive integer.

```javascript
var erlang = new Erlang();

var k = erlang.k;
// returns 1.0

erlang.k = 3.0;

k = erlang.k;
// returns 3.0
```

#### erlang.lambda

Rate parameter of the distribution. `lambda` **must** be a positive number.

```javascript
var erlang = new Erlang( 2, 4.0 );

var lambda = erlang.lambda;
// returns 4.0

erlang.lambda = 3.0;

lambda = erlang.lambda;
// returns 3.0
```

* * *

### Computed Properties

#### Erlang.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var erlang = new Erlang( 4, 12.0 );

var entropy = erlang.entropy;
// returns ~-0.462
```

#### Erlang.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var erlang = new Erlang( 4, 12.0 );

var kurtosis = erlang.kurtosis;
// returns 1.5
```

#### Erlang.prototype.mean

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

```javascript
var erlang = new Erlang( 4, 12.0 );

var mu = erlang.mean;
// returns ~0.333
```

#### Erlang.prototype.mode

Returns the [mode][mode].

```javascript
var erlang = new Erlang( 4, 12.0 );

var mode = erlang.mode;
// returns 0.25
```

#### Erlang.prototype.skewness

Returns the [skewness][skewness].

```javascript
var erlang = new Erlang( 4, 12.0 );

var skewness = erlang.skewness;
// returns 1.0
```

#### Erlang.prototype.stdev

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

```javascript
var erlang = new Erlang( 4, 12.0 );

var s = erlang.stdev;
// returns ~0.167
```

#### Erlang.prototype.variance

Returns the [variance][variance].

```javascript
var erlang = new Erlang( 4, 12.0 );

var s2 = erlang.variance;
// returns ~0.028
```

* * *

### Methods

#### Erlang.prototype.cdf( x )

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

```javascript
var erlang = new Erlang( 2, 4.0 );

var y = erlang.cdf( 0.5 );
// returns ~0.594
```

#### Erlang.prototype.logpdf( x )

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

```javascript
var erlang = new Erlang( 2, 4.0 );

var y = erlang.logpdf( 0.8 );
// returns ~-0.65
```

#### Erlang.prototype.mgf( t )

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

```javascript
var erlang = new Erlang( 2, 4.0 );

var y = erlang.mgf( 0.5 );
// returns ~1.306
```

#### Erlang.prototype.pdf( x )

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

```javascript
var erlang = new Erlang( 2, 4.0 );

var y = erlang.pdf( 0.8 );
// returns ~0.522
```

#### Erlang.prototype.quantile( p )

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

```javascript
var erlang = new Erlang( 2, 4.0 );

var y = erlang.quantile( 0.5 );
// returns ~0.42

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

</section>

<!-- /.usage -->

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<section class="notes">

</section>

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<!-- Package usage examples. -->

* * *

<section class="examples">

## Examples

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

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

var erlang = new Erlang( 2, 4.0 );

var mu = erlang.mean;
// returns 0.5

var mode = erlang.mode;
// returns 0.25

var s2 = erlang.variance;
// returns 0.125

var y = erlang.cdf( 0.8 );
// returns ~0.829
```

</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-erlang-ctor/main/LICENSE

[erlang-distribution]: https://en.wikipedia.org/wiki/Erlang_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

[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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