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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-->\n\n\n<details>\n  <summary>\n    About stdlib...\n  </summary>\n  <p>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.</p>\n  <p>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.</p>\n  <p>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.</p>\n  <p>To join us in bringing numerical computing to the web, get started by checking us out on <a href=\"https://github.com/stdlib-js/stdlib\">GitHub</a>, and please consider <a href=\"https://opencollective.com/stdlib\">financially supporting stdlib</a>. We greatly appreciate your continued support!</p>\n</details>\n\n# Logarithm of Probability Density Function\n\n[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->\n\n> [Beta][beta-distribution] distribution logarithm of probability density function (PDF).\n\n<section class=\"intro\">\n\nThe [probability density function][pdf] (PDF) for a [beta][beta-distribution] random variable is\n\n<!-- <equation 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}} & \\text{ for } x \\in (0,1) \\\\ 0 & \\text{ otherwise } \\end{cases}\" alt=\"Probability density function (PDF) for a beta distribution.\"> -->\n\n<div 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}} &amp; \\text{ for } x \\in (0,1) \\\\ 0 &amp; \\text{ otherwise } \\end{cases}\" data-equation=\"eq:beta_pdf\">\n    <img src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/beta/logpdf/docs/img/equation_beta_pdf.svg\" alt=\"Probability density function (PDF) for a beta distribution.\">\n    <br>\n</div>\n\n<!-- </equation> -->\n\nwhere `alpha > 0` is the first shape parameter and `beta > 0` is the second shape parameter.\n\n</section>\n\n<!-- /.intro -->\n\n<section class=\"installation\">\n\n## Installation\n\n```bash\nnpm install @stdlib/stats-base-dists-beta-logpdf\n```\n\n</section>\n\n<section class=\"usage\">\n\n## Usage\n\n```javascript\nvar logpdf = require( '@stdlib/stats-base-dists-beta-logpdf' );\n```\n\n#### logpdf( x, alpha, beta )\n\nEvaluates the natural logarithm of 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 = logpdf( 0.5, 0.5, 1.0 );\n// returns ~-0.347\n\ny = logpdf( 0.1, 1.0, 1.0 );\n// returns 0.0\n\ny = logpdf( 0.8, 4.0, 2.0 );\n// returns ~0.717\n```\n\nIf provided an input value `x` outside the support `[0,1]`, the function returns `-Infinity`.\n\n```javascript\nvar y = logpdf( -0.1, 1.0, 1.0 );\n// returns -Infinity\n\ny = logpdf( 1.1, 1.0, 1.0 );\n// returns -Infinity\n```\n\nIf provided `NaN` as any argument, the function returns `NaN`.\n\n```javascript\nvar y = logpdf( NaN, 1.0, 1.0 );\n// returns NaN\n\ny = logpdf( 0.0, NaN, 1.0 );\n// returns NaN\n\ny = logpdf( 0.0, 1.0, NaN );\n// returns NaN\n```\n\nIf provided `alpha <= 0`, the function returns `NaN`.\n\n```javascript\nvar y = logpdf( 0.5, 0.0, 1.0 );\n// returns NaN\n\ny = logpdf( 0.5, -1.0, 1.0 );\n// returns NaN\n```\n\nIf provided `beta <= 0`, the function returns `NaN`.\n\n```javascript\nvar y = logpdf( 0.5, 1.0, 0.0 );\n// returns NaN\n\ny = logpdf( 0.5, 1.0, -1.0 );\n// returns NaN\n```\n\n#### logpdf.factory( alpha, beta )\n\nReturns a `function` for evaluating the natural logarithm of the [PDF][pdf] for a [beta][beta-distribution]  distribution with parameters `alpha` (first shape parameter) and `beta` (second shape parameter).\n\n```javascript\nvar mylogPDF = logpdf.factory( 0.5, 0.5 );\n\nvar y = mylogPDF( 0.8 );\n// returns ~-0.228\n\ny = mylogPDF( 0.3 );\n// returns ~-0.364\n```\n\n</section>\n\n<!-- /.usage -->\n\n<section class=\"notes\">\n\n## Notes\n\n-   In virtually all cases, using the `logpdf` or `logcdf` functions is preferable to manually computing the logarithm of the `pdf` or `cdf`, respectively, since the latter is prone to overflow and underflow.\n\n</section>\n\n<!-- /.notes -->\n\n<section class=\"examples\">\n\n## Examples\n\n<!-- eslint no-undef: \"error\" -->\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 logpdf = require( '@stdlib/stats-base-dists-beta-logpdf' );\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, ln(f(x;α,β)): %0.4f', x, alpha, beta, logpdf );\n```\n\n</section>\n\n<!-- /.examples -->\n\n<!-- C interface documentation. -->\n\n* * *\n\n<section class=\"c\">\n\n## C APIs\n\n<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->\n\n<section class=\"intro\">\n\n</section>\n\n<!-- /.intro -->\n\n<!-- C usage documentation. -->\n\n<section class=\"usage\">\n\n### Usage\n\n```c\n#include \"stdlib/stats/base/dists/beta/logpdf.h\"\n```\n\n#### stdlib_base_dists_beta_logpdf( x, alpha, beta )\n\nEvaluates the natural logarithm of the probability density function (logPDF) for a beta distribution with first shape parameter `alpha` and second shape parameter `beta`.\n\n```c\ndouble y = stdlib_base_dists_beta_logpdf( 0.5, 1.0, 1.0 );\n// returns 0.0\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_logpdf( const double x, double alpha, const double beta );\n```\n\n</section>\n\n<!-- /.usage -->\n\n<!-- C API usage notes. Make sure to keep an empty line after the `section`\nelement and another before the `/section` close. -->\n\n<section class=\"notes\">\n\n</section>\n\n<!-- /.notes -->\n\n<!-- C API usage examples. -->\n\n<section class=\"examples\">\n\n### Examples\n\n```c\n#include \"stdlib/stats/base/dists/beta/logpdf.h\"\n#include \"stdlib/constants/float64/eps.h\"\n#include <stdlib.h>\n#include <stdio.h>\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 < 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_logpdf( x, alpha, beta );\n        printf( \"x: %lf, α: %lf, β: %lf, ln(f(x;α,β)): %lf\\n\", x, alpha, beta, y );\n    }\n}\n```\n\n</section>\n\n<!-- /.examples -->\n\n</section>\n\n<!-- /.c -->\n\n<!-- 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. -->\n\n<section class=\"references\">\n\n</section>\n\n<!-- /.references -->\n\n<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->\n\n<section class=\"related\">\n\n</section>\n\n<!-- /.related -->\n\n<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->\n\n\n<section class=\"main-repo\" >\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 &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].\n\n</section>\n\n<!-- /.stdlib -->\n\n<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->\n\n<section class=\"links\">\n\n[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-beta-logpdf.svg\n[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-beta-logpdf\n\n[test-image]: https://github.com/stdlib-js/stats-base-dists-beta-logpdf/actions/workflows/test.yml/badge.svg?branch=v0.3.1\n[test-url]: https://github.com/stdlib-js/stats-base-dists-beta-logpdf/actions/workflows/test.yml?query=branch:v0.3.1\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-beta-logpdf/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-beta-logpdf?branch=main\n\n<!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/stats-base-dists-beta-logpdf.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/stats-base-dists-beta-logpdf/main\n\n-->\n\n[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg\n[chat-url]: https://stdlib.zulipchat.com\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-logpdf/tree/deno\n[deno-readme]: https://github.com/stdlib-js/stats-base-dists-beta-logpdf/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/stats-base-dists-beta-logpdf/tree/umd\n[umd-readme]: https://github.com/stdlib-js/stats-base-dists-beta-logpdf/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/stats-base-dists-beta-logpdf/tree/esm\n[esm-readme]: https://github.com/stdlib-js/stats-base-dists-beta-logpdf/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/stats-base-dists-beta-logpdf/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-beta-logpdf/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</section>\n\n<!-- /.links -->\n","readmeFilename":"README.md"}