{"id":20321340,"url":"https://github.com/stdlib-js/stats-base-dists-poisson","last_synced_at":"2025-08-22T06:42:52.676Z","repository":{"id":41462102,"uuid":"377245166","full_name":"stdlib-js/stats-base-dists-poisson","owner":"stdlib-js","description":"Poisson distribution.","archived":false,"fork":false,"pushed_at":"2025-02-02T14:47:58.000Z","size":2567,"stargazers_count":5,"open_issues_count":0,"forks_count":0,"subscribers_count":3,"default_branch":"main","last_synced_at":"2025-03-20T09:41:12.806Z","etag":null,"topics":["discrete","dist","distribution","javascript","lib","library","node","node-js","nodejs","poisson","probability","standard","statistics","stats","stdlib","univariate"],"latest_commit_sha":null,"homepage":"https://github.com/stdlib-js/stdlib","language":"JavaScript","has_issues":false,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"apache-2.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/stdlib-js.png","metadata":{"files":{"readme":"README.md","changelog":"CHANGELOG.md","contributing":"CONTRIBUTING.md","funding":null,"license":"LICENSE","code_of_conduct":"CODE_OF_CONDUCT.md","threat_model":null,"audit":null,"citation":"CITATION.cff","codeowners":null,"security":"SECURITY.md","support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null},"funding":{"github":["stdlib-js"],"open_collective":"stdlib","tidelift":"npm/@stdlib/stdlib"}},"created_at":"2021-06-15T17:34:42.000Z","updated_at":"2025-02-19T06:51:34.000Z","dependencies_parsed_at":"2023-02-17T04:31:18.154Z","dependency_job_id":"5ecb8d38-d9f4-4527-9302-d54e6337e859","html_url":"https://github.com/stdlib-js/stats-base-dists-poisson","commit_stats":{"total_commits":42,"total_committers":1,"mean_commits":42.0,"dds":0.0,"last_synced_commit":"f137ace084406a3756bc7922fdad3807ec9d102a"},"previous_names":[],"tags_count":21,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-base-dists-poisson","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-base-dists-poisson/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-base-dists-poisson/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-base-dists-poisson/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/stdlib-js","download_url":"https://codeload.github.com/stdlib-js/stats-base-dists-poisson/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":248465317,"owners_count":21108244,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["discrete","dist","distribution","javascript","lib","library","node","node-js","nodejs","poisson","probability","standard","statistics","stats","stdlib","univariate"],"created_at":"2024-11-14T19:14:06.641Z","updated_at":"2025-04-11T19:09:20.109Z","avatar_url":"https://github.com/stdlib-js.png","language":"JavaScript","funding_links":["https://github.com/sponsors/stdlib-js","https://opencollective.com/stdlib","https://tidelift.com/funding/github/npm/@stdlib/stdlib"],"categories":[],"sub_categories":[],"readme":"\u003c!--\n\n@license Apache-2.0\n\nCopyright (c) 2018 The Stdlib Authors.\n\nLicensed under the Apache License, Version 2.0 (the \"License\");\nyou may not use this file except in compliance with the License.\nYou may obtain a copy of the License at\n\n   http://www.apache.org/licenses/LICENSE-2.0\n\nUnless required by applicable law or agreed to in writing, software\ndistributed under the License is distributed on an \"AS IS\" BASIS,\nWITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\nSee the License for the specific language governing permissions and\nlimitations under the License.\n\n--\u003e\n\n\n\u003cdetails\u003e\n  \u003csummary\u003e\n    About stdlib...\n  \u003c/summary\u003e\n  \u003cp\u003eWe 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.\u003c/p\u003e\n  \u003cp\u003eThe 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.\u003c/p\u003e\n  \u003cp\u003eWhen 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.\u003c/p\u003e\n  \u003cp\u003eTo join us in bringing numerical computing to the web, get started by checking us out on \u003ca href=\"https://github.com/stdlib-js/stdlib\"\u003eGitHub\u003c/a\u003e, and please consider \u003ca href=\"https://opencollective.com/stdlib\"\u003efinancially supporting stdlib\u003c/a\u003e. We greatly appreciate your continued support!\u003c/p\u003e\n\u003c/details\u003e\n\n# Poisson\n\n[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] \u003c!-- [![dependencies][dependencies-image]][dependencies-url] --\u003e\n\n\u003e Poisson distribution.\n\n\u003csection class=\"installation\"\u003e\n\n## Installation\n\n```bash\nnpm install @stdlib/stats-base-dists-poisson\n```\n\nAlternatively,\n\n-   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]).\n-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).\n-   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]).\n\nThe [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.\n\nTo 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.\n\n\u003c/section\u003e\n\n\u003csection class=\"usage\"\u003e\n\n## Usage\n\n```javascript\nvar poisson = require( '@stdlib/stats-base-dists-poisson' );\n```\n\n#### poisson\n\nPoisson distribution.\n\n```javascript\nvar dist = poisson;\n// returns {...}\n```\n\nThe namespace contains the following distribution functions:\n\n\u003c!-- \u003ctoc pattern=\"*+(cdf|pmf|mgf|quantile)*\"\u003e --\u003e\n\n\u003cdiv class=\"namespace-toc\"\u003e\n\n-   \u003cspan class=\"signature\"\u003e[`cdf( x, lambda )`][@stdlib/stats/base/dists/poisson/cdf]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ePoisson distribution cumulative distribution function.\u003c/span\u003e\n-   \u003cspan class=\"signature\"\u003e[`logpmf( x, lambda )`][@stdlib/stats/base/dists/poisson/logpmf]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003eevaluate the natural logarithm of the probability mass function (PMF) for a Poisson distribution.\u003c/span\u003e\n-   \u003cspan class=\"signature\"\u003e[`mgf( t, lambda )`][@stdlib/stats/base/dists/poisson/mgf]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ePoisson distribution moment-generating function (MGF).\u003c/span\u003e\n-   \u003cspan class=\"signature\"\u003e[`pmf( x, lambda )`][@stdlib/stats/base/dists/poisson/pmf]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ePoisson distribution probability mass function (PMF).\u003c/span\u003e\n-   \u003cspan class=\"signature\"\u003e[`quantile( p, lambda )`][@stdlib/stats/base/dists/poisson/quantile]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ePoisson distribution quantile function.\u003c/span\u003e\n\n\u003c/div\u003e\n\n\u003c!-- \u003c/toc\u003e --\u003e\n\nThe namespace contains the following functions for calculating distribution properties:\n\n\u003c!-- \u003ctoc pattern=\"*+(entropy|kurtosis|mean|median|mode|skewness|stdev|variance)*\"\u003e --\u003e\n\n\u003cdiv class=\"namespace-toc\"\u003e\n\n-   \u003cspan class=\"signature\"\u003e[`entropy( lambda )`][@stdlib/stats/base/dists/poisson/entropy]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ePoisson distribution entropy.\u003c/span\u003e\n-   \u003cspan class=\"signature\"\u003e[`kurtosis( lambda )`][@stdlib/stats/base/dists/poisson/kurtosis]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ePoisson distribution excess kurtosis.\u003c/span\u003e\n-   \u003cspan class=\"signature\"\u003e[`mean( lambda )`][@stdlib/stats/base/dists/poisson/mean]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ePoisson distribution expected value.\u003c/span\u003e\n-   \u003cspan class=\"signature\"\u003e[`median( lambda )`][@stdlib/stats/base/dists/poisson/median]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ePoisson distribution median.\u003c/span\u003e\n-   \u003cspan class=\"signature\"\u003e[`mode( lambda )`][@stdlib/stats/base/dists/poisson/mode]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ePoisson distribution mode.\u003c/span\u003e\n-   \u003cspan class=\"signature\"\u003e[`skewness( lambda )`][@stdlib/stats/base/dists/poisson/skewness]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ePoisson distribution skewness.\u003c/span\u003e\n-   \u003cspan class=\"signature\"\u003e[`stdev( lambda )`][@stdlib/stats/base/dists/poisson/stdev]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ePoisson distribution standard deviation.\u003c/span\u003e\n-   \u003cspan class=\"signature\"\u003e[`variance( lambda )`][@stdlib/stats/base/dists/poisson/variance]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ePoisson distribution variance.\u003c/span\u003e\n\n\u003c/div\u003e\n\n\u003c!-- \u003c/toc\u003e --\u003e\n\nThe namespace contains a constructor function for creating a [Poisson][poisson-distribution] distribution object.\n\n\u003c!-- \u003ctoc pattern=\"*ctor*\"\u003e --\u003e\n\n\u003cdiv class=\"namespace-toc\"\u003e\n\n-   \u003cspan class=\"signature\"\u003e[`Poisson( [lambda] )`][@stdlib/stats/base/dists/poisson/ctor]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ePoisson distribution constructor.\u003c/span\u003e\n\n\u003c/div\u003e\n\n\u003c!-- \u003c/toc\u003e --\u003e\n\n```javascript\nvar Poisson = require( '@stdlib/stats-base-dists-poisson' ).Poisson;\n\nvar dist = new Poisson( 2.0 );\n\nvar y = dist.pmf( 3.0 );\n// returns ~0.18\n\ny = dist.pmf( 2.3 );\n// returns 0.0\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.usage --\u003e\n\n\u003csection class=\"examples\"\u003e\n\n## Examples\n\n\u003c!-- TODO: better examples --\u003e\n\n\u003c!-- eslint no-undef: \"error\" --\u003e\n\n```javascript\nvar poisson = require( '@stdlib/stats-base-dists-poisson' );\n\n/*\n* Let's take a customer service center example: average rate of customer inquiries is 3 per hour.\n* This situation can be modeled using a Poisson distribution with λ = 3\n*/\n\nvar lambda = 3;\n\n// Mean can be used to calculate the average number of inquiries per hour:\nconsole.log( poisson.mean( lambda ) );\n// =\u003e 3\n\n// Standard deviation can be used to calculate the measure of the spread of inquiries around the mean:\nconsole.log( poisson.stdev( lambda ) );\n// =\u003e ~1.7321\n\n// Variance can be used to calculate the variability of the number of inquiries:\nconsole.log( poisson.variance( lambda ) );\n// =\u003e 3\n\n// PMF can be used to calculate specific number of inquiries in an hour:\nconsole.log( poisson.pmf( 4, lambda ) );\n// =\u003e ~0.1680\n\n// CDF can be used to calculate probability up to certain number of inquiries in an hour:\nconsole.log( poisson.cdf( 2, lambda ) );\n// =\u003e ~0.4232\n\n// Quantile can be used to calculate the number of inquiries at which you can be 80% confident that the actual number will not exceed.\nconsole.log( poisson.quantile( 0.8, lambda ) );\n// =\u003e 4\n\n// MGF can be used for more advanced statistical analyses and generating moments of the distribution.\nconsole.log( poisson.mgf( 1.0, lambda ) );\n// =\u003e ~173.2690\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.examples --\u003e\n\n\u003c!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. --\u003e\n\n\u003csection class=\"related\"\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.related --\u003e\n\n\u003c!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\n\u003csection class=\"main-repo\" \u003e\n\n* * *\n\n## Notice\n\nThis 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.\n\nFor 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].\n\n#### Community\n\n[![Chat][chat-image]][chat-url]\n\n---\n\n## License\n\nSee [LICENSE][stdlib-license].\n\n\n## Copyright\n\nCopyright \u0026copy; 2016-2025. The Stdlib [Authors][stdlib-authors].\n\n\u003c/section\u003e\n\n\u003c!-- /.stdlib --\u003e\n\n\u003c!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"links\"\u003e\n\n[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-poisson.svg\n[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-poisson\n\n[test-image]: https://github.com/stdlib-js/stats-base-dists-poisson/actions/workflows/test.yml/badge.svg?branch=main\n[test-url]: https://github.com/stdlib-js/stats-base-dists-poisson/actions/workflows/test.yml?query=branch:main\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-poisson/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-poisson?branch=main\n\n\u003c!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/stats-base-dists-poisson.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/stats-base-dists-poisson/main\n\n--\u003e\n\n[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg\n[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im\n\n[stdlib]: https://github.com/stdlib-js/stdlib\n\n[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors\n\n[umd]: https://github.com/umdjs/umd\n[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules\n\n[deno-url]: https://github.com/stdlib-js/stats-base-dists-poisson/tree/deno\n[deno-readme]: https://github.com/stdlib-js/stats-base-dists-poisson/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/stats-base-dists-poisson/tree/umd\n[umd-readme]: https://github.com/stdlib-js/stats-base-dists-poisson/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/stats-base-dists-poisson/tree/esm\n[esm-readme]: https://github.com/stdlib-js/stats-base-dists-poisson/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/stats-base-dists-poisson/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-poisson/main/LICENSE\n\n[poisson-distribution]: https://en.wikipedia.org/wiki/Poisson_distribution\n\n\u003c!-- \u003ctoc-links\u003e --\u003e\n\n[@stdlib/stats/base/dists/poisson/ctor]: https://github.com/stdlib-js/stats-base-dists-poisson-ctor\n\n[@stdlib/stats/base/dists/poisson/entropy]: https://github.com/stdlib-js/stats-base-dists-poisson-entropy\n\n[@stdlib/stats/base/dists/poisson/kurtosis]: https://github.com/stdlib-js/stats-base-dists-poisson-kurtosis\n\n[@stdlib/stats/base/dists/poisson/mean]: https://github.com/stdlib-js/stats-base-dists-poisson-mean\n\n[@stdlib/stats/base/dists/poisson/median]: https://github.com/stdlib-js/stats-base-dists-poisson-median\n\n[@stdlib/stats/base/dists/poisson/mode]: https://github.com/stdlib-js/stats-base-dists-poisson-mode\n\n[@stdlib/stats/base/dists/poisson/skewness]: https://github.com/stdlib-js/stats-base-dists-poisson-skewness\n\n[@stdlib/stats/base/dists/poisson/stdev]: https://github.com/stdlib-js/stats-base-dists-poisson-stdev\n\n[@stdlib/stats/base/dists/poisson/variance]: https://github.com/stdlib-js/stats-base-dists-poisson-variance\n\n[@stdlib/stats/base/dists/poisson/cdf]: https://github.com/stdlib-js/stats-base-dists-poisson-cdf\n\n[@stdlib/stats/base/dists/poisson/logpmf]: https://github.com/stdlib-js/stats-base-dists-poisson-logpmf\n\n[@stdlib/stats/base/dists/poisson/mgf]: https://github.com/stdlib-js/stats-base-dists-poisson-mgf\n\n[@stdlib/stats/base/dists/poisson/pmf]: https://github.com/stdlib-js/stats-base-dists-poisson-pmf\n\n[@stdlib/stats/base/dists/poisson/quantile]: https://github.com/stdlib-js/stats-base-dists-poisson-quantile\n\n\u003c!-- \u003c/toc-links\u003e --\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.links --\u003e\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fstats-base-dists-poisson","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fstdlib-js%2Fstats-base-dists-poisson","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fstats-base-dists-poisson/lists"}