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https://github.com/stdlib-js/stats-base-dists-discrete-uniform-logpmf

Natural logarithm of the probability mass function (PMF) for a discrete uniform distribution.
https://github.com/stdlib-js/stats-base-dists-discrete-uniform-logpmf

discrete dist distribution javascript ln log logarithm logpmf natural node node-js nodejs pmf probability statistics stats stdlib symmetric uniform univariate

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Natural logarithm of the probability mass function (PMF) for a discrete uniform distribution.

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README 

        



  

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# Logarithm of Probability Mass 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 mass function][pmf] (PMF) for a [discrete uniform][discrete-uniform-distribution] distribution.



The [probability mass function][pmf] (PMF) for a [discrete uniform][discrete-uniform-distribution] random variable is



```math

P(X=x;a,b)=\begin{cases} \frac{1}{b - a + 1} & \text{for } x \in \{ a, \ldots, b \} \\ 0 & \text{otherwise} \end{cases}

```



where `a` is the minimum support and `b` is the maximum support of the distribution. The parameters must satisfy `a <= b`.



## Installation



```bash

npm install @stdlib/stats-base-dists-discrete-uniform-logpmf

```



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 logpmf = require( '@stdlib/stats-base-dists-discrete-uniform-logpmf' );

```



#### logpmf( x, a, b )



Evaluates the natural logarithm of the [probability mass function][pmf] (PMF) for a [discrete uniform][discrete-uniform-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).



```javascript

var y = logpmf( 2.0, 0, 4 );

// returns ~-1.609



y = logpmf( 5.0, 0, 4 );

// returns -Infinity



y = logpmf( 3, -4, 4 );

// returns ~-2.197

```



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



```javascript

var y = logpmf( NaN, -2, 2 );

// returns NaN



y = logpmf( 1.0, NaN, 4 );

// returns NaN



y = logpmf( 2.0, 0, NaN );

// returns NaN

```



If `a` or `b` is not an integer value, the function returns `NaN`.



```javascript

var y = logpmf( 2.0, 1, 5.5 );

// returns NaN

```



If provided `a > b`, the function returns `NaN`.



```javascript

var y = logpmf( 2.0, 3, 2 );

// returns NaN

```



#### logpmf.factory( a, b )



Returns a `function` for evaluating the [PMF][pmf] for a [discrete uniform][discrete-uniform-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).



```javascript

var myLogPMF = logpmf.factory( 6, 7 );

var y = myLogPMF( 7.0 );

// returns ~-0.693



y = myLogPMF( 5.0 );

// returns -Infinity

```



## Examples



```javascript

var randint = require( '@stdlib/random-base-discrete-uniform' );

var logpmf = require( '@stdlib/stats-base-dists-discrete-uniform-logpmf' );



var randa = randint.factory( 0, 10 );

var randb = randint.factory();

var a;

var b;

var x;

var y;

var i;



for ( i = 0; i < 25; i++ ) {

    a = randa();

    x = randb( a, a+randa() );

    b = randb( a, a+randa() );

    y = logpmf( x, a, b );

    console.log( 'x: %d, a: %d, b: %d, ln(P(X=x;a,b)): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.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]



---



## Copyright



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



[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-discrete-uniform-logpmf.svg

[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-discrete-uniform-logpmf



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

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



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

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

[deno-readme]: https://github.com/stdlib-js/stats-base-dists-discrete-uniform-logpmf/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/stats-base-dists-discrete-uniform-logpmf/tree/umd

[umd-readme]: https://github.com/stdlib-js/stats-base-dists-discrete-uniform-logpmf/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/stats-base-dists-discrete-uniform-logpmf/tree/esm

[esm-readme]: https://github.com/stdlib-js/stats-base-dists-discrete-uniform-logpmf/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/stats-base-dists-discrete-uniform-logpmf/blob/main/branches.md



[pmf]: https://en.wikipedia.org/wiki/Probability_mass_function



[discrete-uniform-distribution]: https://en.wikipedia.org/wiki/Discrete_uniform_distribution