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

Natural logarithm of the probability density function (PDF) for an Erlang distribution.
https://github.com/stdlib-js/stats-base-dists-erlang-logpdf

continuous dist distribution erlang javascript ln log logarithm logpdf natural node node-js nodejs pdf probability statistics stats stdlib univariate

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Natural logarithm of the probability density function (PDF) for an Erlang distribution.

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README 

        



  

    About stdlib...

  

  
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# Logarithm of Probability Density Function



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



> Evaluate the natural logarithm of the probability density function (PDF) for an [Erlang][erlang-distribution] distribution.



The [probability density function][pdf] (PDF) for an [Erlang][erlang-distribution] random variable is



```math

f(x; k,\lambda)={\lambda^k x^{k-1} e^{-\lambda x} \over (k-1)!} 1(x \ge 0)

```



where `k` is the shape parameter and `lambda` is the rate parameter.



## Installation



```bash

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

```



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 logpdf = require( '@stdlib/stats-base-dists-erlang-logpdf' );

```



#### logpdf( x, k, lambda )



Evaluates the natural logarithm of the [probability density function][pdf] (PDF) for an [Erlang][erlang-distribution]  distribution with parameters `k` (shape parameter) and `lambda` (rate parameter).



```javascript

var y = logpdf( 0.1, 1, 1.0 );

// returns ~-0.1



y = logpdf( 0.5, 2, 2.5 );

// returns ~-0.111



y = logpdf( -1.0, 4, 2.0 );

// returns -Infinity

```



If provided `NaN` as any argument, the function returns `NaN`.



```javascript

var y = logpdf( NaN, 1, 1.0 );

// returns NaN



y = logpdf( 0.0, NaN, 1.0 );

// returns NaN



y = logpdf( 0.0, 1, NaN );

// returns NaN

```



If not provided a nonnegative integer for `k`, the function returns `NaN`.



```javascript

var y = logpdf( 2.0, -2, 0.5 );

// returns NaN



y = logpdf( 2.0, 0.5, 0.5 );

// returns NaN

```



If provided `k = 0`, the function evaluates the logarithm of the [PDF][pdf] of a [degenerate distribution][degenerate-distribution] centered at `0`.



```javascript

var y = logpdf( 2.0, 0.0, 2.0 );

// returns -Infinity



y = logpdf( 0.0, 0.0, 2.0 );

// returns Infinity

```



If provided `lambda <= 0`, the function returns `NaN`.



```javascript

var y = logpdf( 2.0, 1, 0.0 );

// returns NaN



y = logpdf( 2.0, 1, -1.0 );

// returns NaN

```



#### logpdf.factory( k, lambda )



Returns a `function` for evaluating the [PDF][pdf] for an [Erlang][erlang-distribution] distribution with parameters `k` (shape parameter) and `lambda` (rate parameter).



```javascript

var mylogpdf = logpdf.factory( 3, 1.5 );



var y = mylogpdf( 1.0 );

// returns ~-0.977



y = mylogpdf( 4.0 );

// returns ~-2.704

```



## Examples



```javascript

var randu = require( '@stdlib/random-base-randu' );

var round = require( '@stdlib/math-base-special-round' );

var logpdf = require( '@stdlib/stats-base-dists-erlang-logpdf' );



var lambda;

var k;

var x;

var y;

var i;



for ( i = 0; i < 20; i++ ) {

    x = randu() * 10.0;

    k = round( randu() * 10.0 );

    lambda = randu() * 5.0;

    y = logpdf( x, k, lambda );

    console.log( 'x: %d, k: %d, λ: %d, ln(f(x;k,λ)): %d', x.toFixed( 4 ), k, lambda.toFixed( 4 ), y.toFixed( 4 ) );

}

```



* * *



## 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-logpdf.svg

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



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

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



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

[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-erlang-logpdf?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-logpdf/tree/deno

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

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

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

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

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

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



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



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



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



[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution