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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 Cumulative Distribution 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> [Gamma][gamma-distribution] distribution logarithm of cumulative distribution function (CDF).\n\n<section class=\"intro\">\n\nThe [cumulative distribution function][cdf] for a [gamma][gamma-distribution] random variable is\n\n<!-- <equation class=\"equation\" label=\"eq:gamma_cdf\" align=\"center\" raw=\"F(x;\\alpha,\\beta) = \\int_0^x f(u;\\alpha,\\beta)\\,du= \\frac{\\gamma(\\alpha, \\beta x)}{\\Gamma(\\alpha)}\" alt=\"Cumulative distribution function for a Gamma distribution.\"> -->\n\n<div class=\"equation\" align=\"center\" data-raw-text=\"F(x;\\alpha,\\beta) = \\int_0^x f(u;\\alpha,\\beta)\\,du= \\frac{\\gamma(\\alpha, \\beta x)}{\\Gamma(\\alpha)}\" data-equation=\"eq:gamma_cdf\">\n    <img src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@9dcb6eb6ab19f2ea81f3bcab5344b29961028a0c/lib/node_modules/@stdlib/stats/base/dists/gamma/logcdf/docs/img/equation_gamma_cdf.svg\" alt=\"Cumulative distribution function for a Gamma distribution.\">\n    <br>\n</div>\n\n<!-- </equation> -->\n\nwhere `alpha` is the shape parameter and `beta` is the rate parameter of the distribution. `gamma` is the lower [incomplete gamma function][@stdlib/math/base/special/gammainc].\n\n</section>\n\n<!-- /.intro -->\n\n<section class=\"installation\">\n\n## Installation\n\n```bash\nnpm install @stdlib/stats-base-dists-gamma-logcdf\n```\n\n</section>\n\n<section class=\"usage\">\n\n## Usage\n\n```javascript\nvar logcdf = require( '@stdlib/stats-base-dists-gamma-logcdf' );\n```\n\n#### logcdf( x, alpha, beta )\n\nEvaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF) for a [gamma][gamma-distribution] distribution with parameters `alpha` (shape parameter) and `beta` (rate parameter).\n\n```javascript\nvar y = logcdf( 2.0, 0.5, 1.0 );\n// returns ~-0.047\n\ny = logcdf( 0.1, 1.0, 1.0 );\n// returns ~-2.352\n\ny = logcdf( -1.0, 4.0, 2.0 );\n// returns -Infinity\n```\n\nIf provided `NaN` as any argument, the function returns `NaN`.\n\n```javascript\nvar y = logcdf( NaN, 1.0, 1.0 );\n// returns NaN\n\ny = logcdf( 0.0, NaN, 1.0 );\n// returns NaN\n\ny = logcdf( 0.0, 1.0, NaN );\n// returns NaN\n```\n\nIf provided `alpha < 0`, the function returns `NaN`.\n\n```javascript\nvar y = logcdf( 2.0, -0.5, 1.0 );\n// returns NaN\n```\n\nIf provided `alpha = 0`, the function evaluates the logarithm of the [CDF][cdf] for a [degenerate distribution][degenerate-distribution] centered at `0`.\n\n```javascript\nvar y = logcdf( 2.0, 0.0, 2.0 );\n// returns 0.0\n\ny = logcdf( -2.0, 0.0, 2.0 );\n// returns -Infinity\n\ny = logcdf( 0.0, 0.0, 2.0 );\n// returns 0.0\n```\n\nIf provided `beta <= 0`, the function returns `NaN`.\n\n```javascript\nvar y = logcdf( 2.0, 1.0, 0.0 );\n// returns NaN\n\ny = logcdf( 2.0, 1.0, -1.0 );\n// returns NaN\n```\n\n#### logcdf.factory( alpha, beta )\n\nReturns a `function` for evaluating the natural logarithm of the [CDF][cdf] for a [gamma][gamma-distribution]  distribution with parameters `alpha` (shape parameter) and `beta` (rate parameter).\n\n```javascript\nvar mylogcdf = logcdf.factory( 3.0, 1.5 );\n\nvar y = mylogcdf( 1.0 );\n// returns ~-1.655\n\ny = mylogcdf( 4.0 );\n// returns ~-0.064\n```\n\n* * *\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/gamma/logcdf.h\"\n```\n\n#### stdlib_base_dists_gamma_logcdf( x, alpha, beta )\n\nEvaluates the natural logarithm of the cumulative distribution function (CDF) for a gamma distribution with shape parameter `alpha` and rate parameter `beta`.\n\n```c\ndouble out = stdlib_base_dists_gamma_logcdf( 2.0, 0.5, 1.0 );\n// returns ~-0.047\n\nout = stdlib_base_dists_gamma_logcdf( 0.1, 1.0, 1.0 );\n// returns ~-2.352\n```\n\nThe function accepts the following arguments:\n\n-   **x**: `[in] double` input value.\n-   **alpha**: `[in] double` shape parameter.\n-   **beta**: `[in] double` rate parameter.\n\n```c\ndouble stdlib_base_dists_gamma_logcdf( const double x, const 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` element 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/gamma/logcdf.h\"\n#include <stdlib.h>\n#include <stdio.h>\n\nstatic double random_uniform( double a, double b ) {\n    double r = ( (double)rand() / ( (double)RAND_MAX + 1.0 ) );\n    return a + ( r * ( b - a ) );\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 < 25; i++ ) {\n        x = random_uniform( 0.0, 2.0 );\n        alpha = random_uniform( 1.0, 10.0 );\n        beta = random_uniform( 1.0, 10.0 );\n        y = stdlib_base_dists_gamma_logcdf( 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<!-- /.usage -->\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 logcdf = require( '@stdlib/stats-base-dists-gamma-logcdf' );\n\nvar opts = {\n    'dtype': 'float64'\n};\nvar x = uniform( 10, 0.0, 3.0, opts );\nvar alpha = uniform( 10, 0.0, 5.0, opts );\nvar beta = uniform( 10, 0.0, 5.0, opts );\n\nlogEachMap( 'x: %0.4f, α: %0.4f, β: %0.4f, ln(f(x;α,β)): %0.4f', x, alpha, beta, logcdf );\n```\n\n</section>\n\n<!-- /.examples -->\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-gamma-logcdf.svg\n[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-gamma-logcdf\n\n[test-image]: https://github.com/stdlib-js/stats-base-dists-gamma-logcdf/actions/workflows/test.yml/badge.svg?branch=v0.3.1\n[test-url]: https://github.com/stdlib-js/stats-base-dists-gamma-logcdf/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-gamma-logcdf/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-gamma-logcdf?branch=main\n\n<!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/stats-base-dists-gamma-logcdf.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/stats-base-dists-gamma-logcdf/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-gamma-logcdf/tree/deno\n[deno-readme]: https://github.com/stdlib-js/stats-base-dists-gamma-logcdf/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/stats-base-dists-gamma-logcdf/tree/umd\n[umd-readme]: https://github.com/stdlib-js/stats-base-dists-gamma-logcdf/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/stats-base-dists-gamma-logcdf/tree/esm\n[esm-readme]: https://github.com/stdlib-js/stats-base-dists-gamma-logcdf/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/stats-base-dists-gamma-logcdf/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-gamma-logcdf/main/LICENSE\n\n[gamma-distribution]: https://en.wikipedia.org/wiki/Gamma_distribution\n\n[cdf]: https://en.wikipedia.org/wiki/Cumulative_Distribution_Function\n\n[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution\n\n[@stdlib/math/base/special/gammainc]: https://www.npmjs.com/package/@stdlib/math-base-special-gammainc\n\n</section>\n\n<!-- /.links -->\n","readmeFilename":"README.md"}