{"id":19755061,"url":"https://github.com/stdlib-js/stats-base-dists-beta-pdf","last_synced_at":"2025-04-30T11:32:16.078Z","repository":{"id":41461901,"uuid":"377244495","full_name":"stdlib-js/stats-base-dists-beta-pdf","owner":"stdlib-js","description":"Beta distribution probability density function (PDF).","archived":false,"fork":false,"pushed_at":"2024-11-01T11:54:10.000Z","size":1513,"stargazers_count":3,"open_issues_count":0,"forks_count":0,"subscribers_count":3,"default_branch":"main","last_synced_at":"2024-11-11T06:52:06.982Z","etag":null,"topics":["beta","continuous","density","dist","distribution","function","javascript","node","node-js","nodejs","pdf","prob","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":"2021-06-15T17:32:22.000Z","updated_at":"2024-11-01T05:58:31.000Z","dependencies_parsed_at":"2023-09-24T11:28:01.906Z","dependency_job_id":"6b94dc50-69ff-499e-b660-deb07c483bc8","html_url":"https://github.com/stdlib-js/stats-base-dists-beta-pdf","commit_stats":{"total_commits":39,"total_committers":1,"mean_commits":39.0,"dds":0.0,"last_synced_commit":"13bbdb287de164abd012c5c272b1439cfc1e8dc3"},"previous_names":[],"tags_count":26,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-base-dists-beta-pdf","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-base-dists-beta-pdf/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-base-dists-beta-pdf/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fstats-base-dists-beta-pdf/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-beta-pdf/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":224208101,"owners_count":17273674,"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":["beta","continuous","density","dist","distribution","function","javascript","node","node-js","nodejs","pdf","prob","probability","statistics","stats","stdlib","univariate"],"created_at":"2024-11-12T03:08:16.308Z","updated_at":"2025-04-30T11:32:16.055Z","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# Probability Density 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 [Beta][beta-distribution] distribution probability density function (PDF).\n\n\u003csection class=\"intro\"\u003e\n\nThe [probability density function][pdf] (PDF) for a [beta][beta-distribution] random variable is\n\n\u003c!-- \u003cequation class=\"equation\" label=\"eq:beta_pdf\" align=\"center\" raw=\"f(x;\\alpha,\\beta)= \\begin{cases} \\frac{\\Gamma(\\alpha + \\beta)}{\\Gamma(\\alpha) + \\Gamma(\\beta)}{x^{\\alpha-1}(1-x)^{\\beta-1}} \u0026 \\text{ for } x \\in (0,1) \\\\ 0 \u0026 \\text{ otherwise } \\end{cases}\" alt=\"Probability density function (PDF) for a beta distribution.\"\u003e --\u003e\n\n```math\nf(x;\\alpha,\\beta)= \\begin{cases} \\frac{\\Gamma(\\alpha + \\beta)}{\\Gamma(\\alpha) + \\Gamma(\\beta)}{x^{\\alpha-1}(1-x)^{\\beta-1}} \u0026 \\text{ for } x \\in (0,1) \\\\ 0 \u0026 \\text{ otherwise } \\end{cases}\n```\n\n\u003c!-- \u003cdiv class=\"equation\" align=\"center\" data-raw-text=\"f(x;\\alpha,\\beta)= \\begin{cases} \\frac{\\Gamma(\\alpha + \\beta)}{\\Gamma(\\alpha) + \\Gamma(\\beta)}{x^{\\alpha-1}(1-x)^{\\beta-1}} \u0026amp; \\text{ for } x \\in (0,1) \\\\ 0 \u0026amp; \\text{ otherwise } \\end{cases}\" data-equation=\"eq:beta_pdf\"\u003e\n    \u003cimg src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/beta/pdf/docs/img/equation_beta_pdf.svg\" alt=\"Probability density function (PDF) for a beta distribution.\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\nwhere `alpha \u003e 0` is the first shape parameter and `beta \u003e 0` is the second shape parameter.\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-beta-pdf\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 pdf = require( '@stdlib/stats-base-dists-beta-pdf' );\n```\n\n#### pdf( x, alpha, beta )\n\nEvaluates the [probability density function][pdf] (PDF) for a [beta][beta-distribution]  distribution with parameters `alpha` (first shape parameter) and `beta` (second shape parameter).\n\n```javascript\nvar y = pdf( 0.5, 0.5, 1.0 );\n// returns ~0.707\n\ny = pdf( 0.1, 1.0, 1.0 );\n// returns 1.0\n\ny = pdf( 0.8, 4.0, 2.0 );\n// returns ~2.048\n```\n\nIf provided a `x` outside the support `[0,1]`, the function returns `0`.\n\n```javascript\nvar y = pdf( -0.1, 1.0, 1.0 );\n// returns 0.0\n\ny = pdf( 1.1, 1.0, 1.0 );\n// returns 0.0\n```\n\nIf provided `NaN` as any argument, the function returns `NaN`.\n\n```javascript\nvar y = pdf( NaN, 1.0, 1.0 );\n// returns NaN\n\ny = pdf( 0.0, NaN, 1.0 );\n// returns NaN\n\ny = pdf( 0.0, 1.0, NaN );\n// returns NaN\n```\n\nIf provided `alpha \u003c= 0`, the function returns `NaN`.\n\n```javascript\nvar y = pdf( 0.5, 0.0, 1.0 );\n// returns NaN\n\ny = pdf( 0.5, -1.0, 1.0 );\n// returns NaN\n```\n\nIf provided `beta \u003c= 0`, the function returns `NaN`.\n\n```javascript\nvar y = pdf( 0.5, 1.0, 0.0 );\n// returns NaN\n\ny = pdf( 0.5, 1.0, -1.0 );\n// returns NaN\n```\n\n#### pdf.factory( alpha, beta )\n\nReturns a `function` for evaluating the [PDF][pdf] for a [beta][beta-distribution] distribution with parameters `alpha` (first shape parameter) and `beta` (second shape parameter).\n\n```javascript\nvar mypdf = pdf.factory( 0.5, 0.5 );\n\nvar y = mypdf( 0.8 );\n// returns ~0.796\n\ny = mypdf( 0.3 );\n// returns ~0.695\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 uniform = require( '@stdlib/random-array-uniform' );\nvar logEachMap = require( '@stdlib/console-log-each-map' );\nvar EPS = require( '@stdlib/constants-float64-eps' );\nvar pdf = require( '@stdlib/stats-base-dists-beta-pdf' );\n\nvar opts = {\n    'dtype': 'float64'\n};\nvar alpha = uniform( 10, EPS, 5.0, opts );\nvar beta = uniform( 10, EPS, 5.0, opts );\nvar x = uniform( 10, 0.0, 1.0, opts );\n\nlogEachMap( 'x: %0.4f, α: %0.4f, β: %0.4f, f(x;α,β): %0.4f', x, alpha, beta, pdf );\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.examples --\u003e\n\n\u003c!-- C interface documentation. --\u003e\n\n* * *\n\n\u003csection class=\"c\"\u003e\n\n## C APIs\n\n\u003c!-- Section to include introductory text.  Make sure to keep an empty line after the intro `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"intro\"\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.intro --\u003e\n\n\u003c!-- C usage documentation. --\u003e\n\n\u003csection class=\"usage\"\u003e\n\n### Usage\n\n```c\n#include \"stdlib/stats/base/dists/beta/pdf.h\"\n```\n\n#### stdlib_base_dists_beta_pdf( x, alpha, beta )\n\nEvaluates the probability density function (PDF) for a beta distribution with first shape parameter `alpha` and second shape parameter `beta`.\n\n```c\ndouble y = stdlib_base_dists_beta_pdf( 0.5, 1.0, 1.0 );\n// returns 1.0\n```\n\nThe function accepts the following arguments:\n\n-   **x**: `[in] double` input value.\n-   **alpha**: `[in] double` first shape parameter.\n-   **beta**: `[in] double` second shape parameter.\n\n```c\ndouble stdlib_base_dists_beta_pdf( const double x, double alpha, const double beta );\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.usage --\u003e\n\n\u003c!-- C API usage notes. Make sure to keep an empty line after the `section`\nelement and another before the `/section` close. --\u003e\n\n\u003csection class=\"notes\"\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.notes --\u003e\n\n\u003c!-- C API usage examples. --\u003e\n\n\u003csection class=\"examples\"\u003e\n\n### Examples\n\n```c\n#include \"stdlib/stats/base/dists/beta/pdf.h\"\n#include \"stdlib/constants/float64/eps.h\"\n#include \u003cstdlib.h\u003e\n#include \u003cstdio.h\u003e\n\nstatic double random_uniform( const double min, const double max ) {\n    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );\n    return min + ( v*(max-min) );\n}\n\nint main( void ) {\n    double alpha;\n    double beta;\n    double x;\n    double y;\n    int i;\n\n    for ( i = 0; i \u003c 10; i++ ) {\n        x = random_uniform( 0.0, 1.0 );\n        alpha = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 5.0 );\n        beta = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 5.0 );\n        y = stdlib_base_dists_beta_pdf( x, alpha, beta );\n        printf( \"x: %lf, α: %lf, β: %lf, f(x;α,β): %lf\\n\", x, alpha, beta, y );\n    }\n}\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.examples --\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.c --\u003e\n\n\u003c!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"references\"\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.references --\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-beta-pdf.svg\n[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-beta-pdf\n\n[test-image]: https://github.com/stdlib-js/stats-base-dists-beta-pdf/actions/workflows/test.yml/badge.svg?branch=main\n[test-url]: https://github.com/stdlib-js/stats-base-dists-beta-pdf/actions/workflows/test.yml?query=branch:main\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-beta-pdf/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-beta-pdf?branch=main\n\n\u003c!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/stats-base-dists-beta-pdf.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/stats-base-dists-beta-pdf/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-beta-pdf/tree/deno\n[deno-readme]: https://github.com/stdlib-js/stats-base-dists-beta-pdf/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/stats-base-dists-beta-pdf/tree/umd\n[umd-readme]: https://github.com/stdlib-js/stats-base-dists-beta-pdf/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/stats-base-dists-beta-pdf/tree/esm\n[esm-readme]: https://github.com/stdlib-js/stats-base-dists-beta-pdf/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/stats-base-dists-beta-pdf/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-beta-pdf/main/LICENSE\n\n[beta-distribution]: https://en.wikipedia.org/wiki/Beta_distribution\n\n[pdf]: https://en.wikipedia.org/wiki/Probability_density_function\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-beta-pdf","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fstdlib-js%2Fstats-base-dists-beta-pdf","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fstats-base-dists-beta-pdf/lists"}