https://github.com/stdlib-js/stats-base-dists-binomial-logpmf
Natural logarithm of the probability mass function (PMF) for a binomial distribution.
https://github.com/stdlib-js/stats-base-dists-binomial-logpmf
bernoulli binom binomial coin-flip dist distribution failure javascript logpmf node node-js nodejs pmf prob probability statistics stats stdlib success trials
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Natural logarithm of the probability mass function (PMF) for a binomial distribution.
- Host: GitHub
- URL: https://github.com/stdlib-js/stats-base-dists-binomial-logpmf
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-15T17:32:51.000Z (over 4 years ago)
- Default Branch: main
- Last Pushed: 2025-09-07T16:12:26.000Z (29 days ago)
- Last Synced: 2025-09-26T05:59:55.651Z (11 days ago)
- Topics: bernoulli, binom, binomial, coin-flip, dist, distribution, failure, javascript, logpmf, node, node-js, nodejs, pmf, prob, probability, statistics, stats, stdlib, success, trials
- Language: JavaScript
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 1.29 MB
- Stars: 1
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
- Notice: NOTICE
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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) for a [binomial][binomial-distribution] distribution.
The [probability mass function][pmf] (PMF) for a [binomial][binomial-distribution] random variable is
```math
f(x;n,p)=P(X=x;n,p)=\begin{cases} \textstyle {n \choose x}\, p^x (1-p)^{n-x} & \text{ for } x = 0,1,2,\ldots \\ 0 & \text{ otherwise} \end{cases}
```
where `n` is the number of trials and `0 <= p <= 1` is the success probability.
## Installation
```bash
npm install @stdlib/stats-base-dists-binomial-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-binomial-logpmf' );
```
#### logpmf( x, n, p )
Evaluates the natural logarithm of the [probability mass function][pmf] (PMF) for a [binomial][binomial-distribution] distribution with number of trials `n` and success probability `p`.
```javascript
var y = logpmf( 3.0, 20, 0.2 );
// returns ~-1.583
y = logpmf( 21.0, 20, 0.2 );
// returns -Infinity
y = logpmf( 5.0, 10, 0.4 );
// returns ~-1.606
y = logpmf( 0.0, 10, 0.4 );
// returns ~-5.108
```
If provided `NaN` as any argument, the function returns `NaN`.
```javascript
var y = logpmf( NaN, 20, 0.5 );
// returns NaN
y = logpmf( 0.0, NaN, 0.5 );
// returns NaN
y = logpmf( 0.0, 20, NaN );
// returns NaN
```
If provided a number of trials `n` which is not a nonnegative integer, the function returns `NaN`.
```javascript
var y = logpmf( 2.0, 1.5, 0.5 );
// returns NaN
y = logpmf( 2.0, -2.0, 0.5 );
// returns NaN
```
If provided a success probability `p` outside of `[0,1]`, the function returns `NaN`.
```javascript
var y = logpmf( 2.0, 20, -1.0 );
// returns NaN
y = logpmf( 2.0, 20, 1.5 );
// returns NaN
```
#### logpmf.factory( n, p )
Returns a function for evaluating the [probability mass function][pmf] (PMF) of a [binomial][binomial-distribution] distribution with number of trials `n` and success probability `p`.
```javascript
var mylogpmf = logpmf.factory( 10, 0.5 );
var y = mylogpmf( 3.0 );
// returns ~-2.144
y = mylogpmf( 5.0 );
// returns ~-1.402
```
## Examples
```javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var logpmf = require( '@stdlib/stats-base-dists-binomial-logpmf' );
var opts = {
'dtype': 'float64'
};
var x = discreteUniform( 10, 0, 20, opts );
var n = discreteUniform( 10, 0, 100, opts );
var p = uniform( 10, 0.0, 1.0, opts );
logEachMap( 'x: %0.4f, n: %0.4f, p: %0.4f, ln(P(X = x;n,p)): %0.4f', x, n, p, logpmf );
```
* * *
## 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 © 2016-2025. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-binomial-logpmf.svg
[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-binomial-logpmf
[test-image]: https://github.com/stdlib-js/stats-base-dists-binomial-logpmf/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/stats-base-dists-binomial-logpmf/actions/workflows/test.yml?query=branch:main
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-binomial-logpmf/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-binomial-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-binomial-logpmf/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-binomial-logpmf/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-binomial-logpmf/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-binomial-logpmf/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-binomial-logpmf/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-binomial-logpmf/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-binomial-logpmf/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-binomial-logpmf/main/LICENSE
[binomial-distribution]: https://en.wikipedia.org/wiki/Binomial_distribution
[pmf]: https://en.wikipedia.org/wiki/Probability_mass_function