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https://github.com/stdlib-js/stats-base-dists-poisson
Poisson distribution.
https://github.com/stdlib-js/stats-base-dists-poisson
discrete dist distribution javascript lib library node node-js nodejs poisson probability standard statistics stats stdlib univariate
Last synced: 1 day ago
JSON representation
Poisson distribution.
- Host: GitHub
- URL: https://github.com/stdlib-js/stats-base-dists-poisson
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-15T17:34:42.000Z (over 3 years ago)
- Default Branch: main
- Last Pushed: 2024-11-01T11:48:29.000Z (15 days ago)
- Last Synced: 2024-11-08T01:40:12.351Z (8 days ago)
- Topics: discrete, dist, distribution, javascript, lib, library, node, node-js, nodejs, poisson, probability, standard, statistics, stats, stdlib, univariate
- Language: JavaScript
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 2.38 MB
- Stars: 4
- 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
Awesome Lists containing this project
README
About stdlib...
We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.
The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.
When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.
To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!
# Poisson
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> Poisson distribution.
## Installation
```bash
npm install @stdlib/stats-base-dists-poisson
```
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 poisson = require( '@stdlib/stats-base-dists-poisson' );
```
#### poisson
Poisson distribution.
```javascript
var dist = poisson;
// returns {...}
```
The namespace contains the following distribution functions:
- [`cdf( x, lambda )`][@stdlib/stats/base/dists/poisson/cdf]: Poisson distribution cumulative distribution function.
- [`logpmf( x, lambda )`][@stdlib/stats/base/dists/poisson/logpmf]: evaluate the natural logarithm of the probability mass function (PMF) for a Poisson distribution.
- [`mgf( t, lambda )`][@stdlib/stats/base/dists/poisson/mgf]: Poisson distribution moment-generating function (MGF).
- [`pmf( x, lambda )`][@stdlib/stats/base/dists/poisson/pmf]: Poisson distribution probability mass function (PMF).
- [`quantile( p, lambda )`][@stdlib/stats/base/dists/poisson/quantile]: Poisson distribution quantile function.
The namespace contains the following functions for calculating distribution properties:
- [`entropy( lambda )`][@stdlib/stats/base/dists/poisson/entropy]: Poisson distribution entropy.
- [`kurtosis( lambda )`][@stdlib/stats/base/dists/poisson/kurtosis]: Poisson distribution excess kurtosis.
- [`mean( lambda )`][@stdlib/stats/base/dists/poisson/mean]: Poisson distribution expected value.
- [`median( lambda )`][@stdlib/stats/base/dists/poisson/median]: Poisson distribution median.
- [`mode( lambda )`][@stdlib/stats/base/dists/poisson/mode]: Poisson distribution mode.
- [`skewness( lambda )`][@stdlib/stats/base/dists/poisson/skewness]: Poisson distribution skewness.
- [`stdev( lambda )`][@stdlib/stats/base/dists/poisson/stdev]: Poisson distribution standard deviation.
- [`variance( lambda )`][@stdlib/stats/base/dists/poisson/variance]: Poisson distribution variance.
The namespace contains a constructor function for creating a [Poisson][poisson-distribution] distribution object.
- [`Poisson( [lambda] )`][@stdlib/stats/base/dists/poisson/ctor]: Poisson distribution constructor.
```javascript
var Poisson = require( '@stdlib/stats-base-dists-poisson' ).Poisson;
var dist = new Poisson( 2.0 );
var y = dist.pmf( 3.0 );
// returns ~0.18
y = dist.pmf( 2.3 );
// returns 0.0
```
## Examples
```javascript
var poisson = require( '@stdlib/stats-base-dists-poisson' );
/*
* Let's take a customer service center example: average rate of customer inquiries is 3 per hour.
* This situation can be modeled using a Poisson distribution with λ = 3
*/
var lambda = 3;
// Mean can be used to calculate the average number of inquiries per hour:
console.log( poisson.mean( lambda ) );
// => 3
// Standard deviation can be used to calculate the measure of the spread of inquiries around the mean:
console.log( poisson.stdev( lambda ) );
// => ~1.7321
// Variance can be used to calculate the variability of the number of inquiries:
console.log( poisson.variance( lambda ) );
// => 3
// PMF can be used to calculate specific number of inquiries in an hour:
console.log( poisson.pmf( 4, lambda ) );
// => ~0.1680
// CDF can be used to calculate probability up to certain number of inquiries in an hour:
console.log( poisson.cdf( 2, lambda ) );
// => ~0.4232
// Quantile can be used to calculate the number of inquiries at which you can be 80% confident that the actual number will not exceed.
console.log( poisson.quantile( 0.8, lambda ) );
// => 4
// MGF can be used for more advanced statistical analyses and generating moments of the distribution.
console.log( poisson.mgf( 1.0, lambda ) );
// => ~173.2690
```
* * *
## 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-poisson.svg
[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-poisson
[test-image]: https://github.com/stdlib-js/stats-base-dists-poisson/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/stats-base-dists-poisson/actions/workflows/test.yml?query=branch:main
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-poisson/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-poisson?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-poisson/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-poisson/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-poisson/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-poisson/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-poisson/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-poisson/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-poisson/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-poisson/main/LICENSE
[poisson-distribution]: https://en.wikipedia.org/wiki/Poisson_distribution
[@stdlib/stats/base/dists/poisson/ctor]: https://github.com/stdlib-js/stats-base-dists-poisson-ctor
[@stdlib/stats/base/dists/poisson/entropy]: https://github.com/stdlib-js/stats-base-dists-poisson-entropy
[@stdlib/stats/base/dists/poisson/kurtosis]: https://github.com/stdlib-js/stats-base-dists-poisson-kurtosis
[@stdlib/stats/base/dists/poisson/mean]: https://github.com/stdlib-js/stats-base-dists-poisson-mean
[@stdlib/stats/base/dists/poisson/median]: https://github.com/stdlib-js/stats-base-dists-poisson-median
[@stdlib/stats/base/dists/poisson/mode]: https://github.com/stdlib-js/stats-base-dists-poisson-mode
[@stdlib/stats/base/dists/poisson/skewness]: https://github.com/stdlib-js/stats-base-dists-poisson-skewness
[@stdlib/stats/base/dists/poisson/stdev]: https://github.com/stdlib-js/stats-base-dists-poisson-stdev
[@stdlib/stats/base/dists/poisson/variance]: https://github.com/stdlib-js/stats-base-dists-poisson-variance
[@stdlib/stats/base/dists/poisson/cdf]: https://github.com/stdlib-js/stats-base-dists-poisson-cdf
[@stdlib/stats/base/dists/poisson/logpmf]: https://github.com/stdlib-js/stats-base-dists-poisson-logpmf
[@stdlib/stats/base/dists/poisson/mgf]: https://github.com/stdlib-js/stats-base-dists-poisson-mgf
[@stdlib/stats/base/dists/poisson/pmf]: https://github.com/stdlib-js/stats-base-dists-poisson-pmf
[@stdlib/stats/base/dists/poisson/quantile]: https://github.com/stdlib-js/stats-base-dists-poisson-quantile