{"id":22147170,"url":"https://github.com/stdlib-js/stats-base-dists-negative-binomial-cdf","last_synced_at":"2025-07-26T02:31:39.872Z","repository":{"id":41404595,"uuid":"377247031","full_name":"stdlib-js/stats-base-dists-negative-binomial-cdf","owner":"stdlib-js","description":"Negative binomial distribution cumulative distribution function (CDF).","archived":false,"fork":false,"pushed_at":"2024-12-01T11:49:51.000Z","size":2332,"stargazers_count":2,"open_issues_count":0,"forks_count":0,"subscribers_count":3,"default_branch":"main","last_synced_at":"2024-12-01T12:36:52.737Z","etag":null,"topics":["binomial","cdf","cumulative-distribution","discrete","dist","distribution","distribution-function","javascript","negative","node","node-js","nodejs","probability","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":"2021-06-15T17:41:39.000Z","updated_at":"2024-12-01T06:01:06.000Z","dependencies_parsed_at":"2023-12-01T06:25:07.529Z","dependency_job_id":"b7ec32f2-350e-4d95-962f-8628f5f89638","html_url":"https://github.com/stdlib-js/stats-base-dists-negative-binomial-cdf","commit_stats":{"total_commits":47,"total_committers":1,"mean_commits":47.0,"dds":0.0,"last_synced_commit":"14fa4463837a439b2dbb0b13ab4d95b944797b36"},"previous_names":[],"tags_count":18,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-base-dists-negative-binomial-cdf","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-base-dists-negative-binomial-cdf/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-base-dists-negative-binomial-cdf/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-base-dists-negative-binomial-cdf/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-negative-binomial-cdf/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":227561619,"owners_count":17787048,"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":["binomial","cdf","cumulative-distribution","discrete","dist","distribution","distribution-function","javascript","negative","node","node-js","nodejs","probability","statistics","stats","stdlib","univariate"],"created_at":"2024-12-01T23:13:44.373Z","updated_at":"2025-07-26T02:31:39.856Z","avatar_url":"https://github.com/stdlib-js.png","language":"JavaScript","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# Cumulative Distribution Function\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 [Negative binomial][negative-binomial-distribution] distribution [cumulative distribution function][cdf].\n\n\u003csection class=\"intro\"\u003e\n\nThe [cumulative distribution function][cdf] for a [negative binomial][negative-binomial-distribution] random variable `X` is\n\n\u003c!-- \u003cequation class=\"equation\" label=\"eq:negative_binomial_cdf\" align=\"center\" raw=\"F(x;r,p)=1-I_p(x+1,r)\" alt=\"Cumulative distribution function for a negative binomial distribution.\"\u003e --\u003e\n\n```math\nF(x;r,p)=1-I_p(x+1,r)\n```\n\n\u003c!-- \u003cdiv class=\"equation\" align=\"center\" data-raw-text=\"F(x;r,p)=1-I_p(x+1,r)\" data-equation=\"eq:negative_binomial_cdf\"\u003e\n    \u003cimg src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/negative-binomial/cdf/docs/img/equation_negative_binomial_cdf.svg\" alt=\"Cumulative distribution function for a negative binomial distribution.\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\nwhere `r` is the number of successes until experiment is stopped, `p` is the success probability in each trial and `I` is the [lower regularized incomplete beta function][incomplete-beta]. The random variable `X` denotes the number of failures until the `r` success is reached.\n\n\u003c/section\u003e\n\n\u003c!-- /.intro --\u003e\n\n\u003csection class=\"installation\"\u003e\n\n## Installation\n\n```bash\nnpm install @stdlib/stats-base-dists-negative-binomial-cdf\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 cdf = require( '@stdlib/stats-base-dists-negative-binomial-cdf' );\n```\n\n#### cdf( x, r, p )\n\nEvaluates the [cumulative distribution function][cdf] for a [negative binomial][negative-binomial-distribution] distribution with number of successes until experiment is stopped `r` and success probability `p`.\n\n```javascript\nvar y = cdf( 5.0, 20.0, 0.8 );\n// returns ~0.617\n\ny = cdf( 21.0, 20.0, 0.5 );\n// returns ~0.622\n\ny = cdf( 5.0, 10.0, 0.4 );\n// returns ~0.034\n\ny = cdf( 0.0, 10.0, 0.9 );\n// returns ~0.349\n```\n\nWhile `r` can be interpreted as the number of successes until the experiment is stopped, the [negative binomial][negative-binomial-distribution] distribution is also defined for non-integers `r`. In this case, `r` denotes shape parameter of the [gamma mixing distribution][negative-binomial-mixture-representation].\n\n```javascript\nvar y = cdf( 21.0, 15.5, 0.5 );\n// returns ~0.859\n\ny = cdf( 5.0, 7.4, 0.4 );\n// returns ~0.131\n```\n\nIf provided a `r` which is not a positive number, the function returns `NaN`.\n\n```javascript\nvar y = cdf( 2.0, 0.0, 0.5 );\n// returns NaN\n\ny = cdf( 2.0, -2.0, 0.5 );\n// returns NaN\n```\n\nIf provided `NaN` as any argument, the function returns `NaN`.\n\n```javascript\nvar y = cdf( NaN, 20.0, 0.5 );\n// returns NaN\n\ny = cdf( 0.0, NaN, 0.5 );\n// returns NaN\n\ny = cdf( 0.0, 20.0, NaN );\n// returns NaN\n```\n\nIf provided a success probability `p` outside of `[0,1]`, the function returns `NaN`.\n\n```javascript\nvar y = cdf( 2.0, 20, -1.0 );\n// returns NaN\n\ny = cdf( 2.0, 20, 1.5 );\n// returns NaN\n```\n\n#### cdf.factory( r, p )\n\nReturns a function for evaluating the [cumulative distribution function][cdf] of a [negative binomial][negative-binomial-distribution] distribution with number of successes until experiment is stopped `r` and success probability `p`.\n\n```javascript\nvar mycdf = cdf.factory( 10, 0.5 );\nvar y = mycdf( 3.0 );\n// returns ~0.046\n\ny = mycdf( 11.0 );\n// returns ~0.668\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.usage --\u003e\n\n\u003csection class=\"examples\"\u003e\n\n## Examples\n\n\u003c!-- eslint no-undef: \"error\" --\u003e\n\n```javascript\nvar randu = require( '@stdlib/random-base-randu' );\nvar cdf = require( '@stdlib/stats-base-dists-negative-binomial-cdf' );\n\nvar i;\nvar r;\nvar p;\nvar x;\nvar y;\n\nfor ( i = 0; i \u003c 10; i++ ) {\n    x = randu() * 50;\n    r = randu() * 50;\n    p = randu();\n    y = cdf( x, r, p );\n    console.log( 'x: %d, r: %d, p: %d, F(x;r,p): %d', x.toFixed( 4 ), r.toFixed( 4 ), p.toFixed( 4 ), y.toFixed( 4 ) );\n}\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-negative-binomial-cdf.svg\n[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-negative-binomial-cdf\n\n[test-image]: https://github.com/stdlib-js/stats-base-dists-negative-binomial-cdf/actions/workflows/test.yml/badge.svg?branch=main\n[test-url]: https://github.com/stdlib-js/stats-base-dists-negative-binomial-cdf/actions/workflows/test.yml?query=branch:main\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-negative-binomial-cdf/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-negative-binomial-cdf?branch=main\n\n\u003c!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/stats-base-dists-negative-binomial-cdf.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/stats-base-dists-negative-binomial-cdf/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-negative-binomial-cdf/tree/deno\n[deno-readme]: https://github.com/stdlib-js/stats-base-dists-negative-binomial-cdf/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/stats-base-dists-negative-binomial-cdf/tree/umd\n[umd-readme]: https://github.com/stdlib-js/stats-base-dists-negative-binomial-cdf/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/stats-base-dists-negative-binomial-cdf/tree/esm\n[esm-readme]: https://github.com/stdlib-js/stats-base-dists-negative-binomial-cdf/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/stats-base-dists-negative-binomial-cdf/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-negative-binomial-cdf/main/LICENSE\n\n[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function\n\n[incomplete-beta]: https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function\n\n[negative-binomial-mixture-representation]: https://en.wikipedia.org/wiki/Negative_binomial_distribution#Gamma.E2.80.93Poisson_mixture\n\n[negative-binomial-distribution]: https://en.wikipedia.org/wiki/Negative_binomial_distribution\n\n\u003c/section\u003e\n\n\u003c!-- /.links --\u003e\n","funding_links":["https://github.com/sponsors/stdlib-js","https://opencollective.com/stdlib","https://tidelift.com/funding/github/npm/@stdlib/stdlib"],"categories":[],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fstats-base-dists-negative-binomial-cdf","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fstdlib-js%2Fstats-base-dists-negative-binomial-cdf","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fstats-base-dists-negative-binomial-cdf/lists"}