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https://github.com/stdlib-js/stats-base-dists-erlang-ctor

Erlang distribution constructor.
https://github.com/stdlib-js/stats-base-dists-erlang-ctor

cdf class constructor ctor dist distribution erlang javascript node node-js nodejs object pdf prob probability properties quantile statistics stats stdlib

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Erlang distribution constructor.

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README 

        



  

    About stdlib...

  

  
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# Erlang



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



> Erlang distribution constructor.



## Installation



```bash

npm install @stdlib/stats-base-dists-erlang-ctor

```



Alternatively,



-   To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).

-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).

-   For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).



The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.



To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.



## 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

```



* * *



## Examples



```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

```



* * *



## 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 © 2016-2024. The Stdlib [Authors][stdlib-authors].



[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-erlang-ctor.svg

[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-erlang-ctor



[test-image]: https://github.com/stdlib-js/stats-base-dists-erlang-ctor/actions/workflows/test.yml/badge.svg?branch=main

[test-url]: https://github.com/stdlib-js/stats-base-dists-erlang-ctor/actions/workflows/test.yml?query=branch:main



[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-erlang-ctor/main.svg

[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-erlang-ctor?branch=main



[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg

[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im



[stdlib]: https://github.com/stdlib-js/stdlib



[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors



[umd]: https://github.com/umdjs/umd

[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules



[deno-url]: https://github.com/stdlib-js/stats-base-dists-erlang-ctor/tree/deno

[deno-readme]: https://github.com/stdlib-js/stats-base-dists-erlang-ctor/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/stats-base-dists-erlang-ctor/tree/umd

[umd-readme]: https://github.com/stdlib-js/stats-base-dists-erlang-ctor/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/stats-base-dists-erlang-ctor/tree/esm

[esm-readme]: https://github.com/stdlib-js/stats-base-dists-erlang-ctor/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/stats-base-dists-erlang-ctor/blob/main/branches.md



[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