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Stdlib Authors","url":"https://github.com/stdlib-js/stdlib/graphs/contributors"},"license":"Apache-2.0","homepage":"https://stdlib.io","keywords":["stdlib","stdmath","statistics","stats","distribution","dist","object","class","constructor","ctor","probability","prob","beta","cdf","pdf","quantile","properties","props","univariate","continuous"],"repository":{"type":"git","url":"git://github.com/stdlib-js/stats-base-dists-beta-ctor.git"},"description":"Beta distribution constructor.","contributors":[{"name":"The Stdlib Authors","url":"https://github.com/stdlib-js/stdlib/graphs/contributors"}],"maintainers":[{"name":"stdlib-bot","email":"kgryte+stdlibbot@gmail.com"},{"name":"kgryte","email":"kgryte@gmail.com"},{"name":"planeshifter","email":"pgb@andrew.cmu.edu"},{"name":"rreusser","email":"rsreusser@gmail.com"}],"readme":"<!--\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-->\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# Beta\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 distribution constructor.\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<!-- Package usage documentation. -->\n\n<section class=\"installation\">\n\n## Installation\n\n```bash\nnpm install @stdlib/stats-base-dists-beta-ctor\n```\n\n</section>\n\n<section class=\"usage\">\n\n## Usage\n\n```javascript\nvar Beta = require( '@stdlib/stats-base-dists-beta-ctor' );\n```\n\n#### Beta( \\[alpha, beta] )\n\nReturns a [beta][beta-distribution] distribution object.\n\n```javascript\nvar beta = new Beta();\n\nvar mu = beta.mean;\n// returns 0.5\n```\n\nBy default, `alpha = 1.0` and `beta = 1.0`. To create a distribution having a different `alpha` (first shape parameter) and `beta` (second shape parameter), provide the corresponding arguments.\n\n```javascript\nvar beta = new Beta( 2.0, 4.0 );\n\nvar mu = beta.mean;\n// returns ~0.333\n```\n\n* * *\n\n## beta\n\nA [beta][beta-distribution] distribution object has the following properties and methods...\n\n### Writable Properties\n\n#### beta.alpha\n\nFirst shape parameter of the distribution. `alpha` **must** be a positive number.\n\n```javascript\nvar beta = new Beta();\n\nvar alpha = beta.alpha;\n// returns 1.0\n\nbeta.alpha = 3.0;\n\nalpha = beta.alpha;\n// returns 3.0\n```\n\n#### beta.beta\n\nSecond shape parameter of the distribution. `beta` **must** be a positive number.\n\n```javascript\nvar beta = new Beta( 2.0, 4.0 );\n\nvar b = beta.beta;\n// returns 4.0\n\nbeta.beta = 3.0;\n\nb = beta.beta;\n// returns 3.0\n```\n\n* * *\n\n### Computed Properties\n\n#### Beta.prototype.entropy\n\nReturns the [differential entropy][entropy].\n\n```javascript\nvar beta = new Beta( 4.0, 12.0 );\n\nvar entropy = beta.entropy;\n// returns ~-0.869\n```\n\n#### Beta.prototype.kurtosis\n\nReturns the [excess kurtosis][kurtosis].\n\n```javascript\nvar beta = new Beta( 4.0, 12.0 );\n\nvar kurtosis = beta.kurtosis;\n// returns ~0.082\n```\n\n#### Beta.prototype.mean\n\nReturns the [expected value][expected-value].\n\n```javascript\nvar beta = new Beta( 4.0, 12.0 );\n\nvar mu = beta.mean;\n// returns 0.25\n```\n\n#### Beta.prototype.median\n\nReturns the [median][median].\n\n```javascript\nvar beta = new Beta( 4.0, 12.0 );\n\nvar median = beta.median;\n// returns ~0.239\n```\n\n#### Beta.prototype.mode\n\nReturns the [mode][mode].\n\n```javascript\nvar beta = new Beta( 4.0, 12.0 );\n\nvar mode = beta.mode;\n// returns ~0.214\n```\n\n#### Beta.prototype.skewness\n\nReturns the [skewness][skewness].\n\n```javascript\nvar beta = new Beta( 4.0, 12.0 );\n\nvar skewness = beta.skewness;\n// returns ~0.529\n```\n\n#### Beta.prototype.stdev\n\nReturns the [standard deviation][standard-deviation].\n\n```javascript\nvar beta = new Beta( 4.0, 12.0 );\n\nvar s = beta.stdev;\n// returns ~0.105\n```\n\n#### Beta.prototype.variance\n\nReturns the [variance][variance].\n\n```javascript\nvar beta = new Beta( 4.0, 12.0 );\n\nvar s2 = beta.variance;\n// returns ~0.011\n```\n\n* * *\n\n### Methods\n\n#### Beta.prototype.cdf( x )\n\nEvaluates the [cumulative distribution function][cdf] (CDF).\n\n```javascript\nvar beta = new Beta( 2.0, 4.0 );\n\nvar y = beta.cdf( 0.5 );\n// returns ~0.813\n```\n\n#### Beta.prototype.logcdf( x )\n\nEvaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF).\n\n```javascript\nvar beta = new Beta( 2.0, 4.0 );\n\nvar y = beta.logcdf( 0.5 );\n// returns ~-0.208\n```\n\n#### Beta.prototype.logpdf( x )\n\nEvaluates the natural logarithm of the [probability density function][pdf] (PDF).\n\n```javascript\nvar beta = new Beta( 2.0, 4.0 );\n\nvar y = beta.logpdf( 0.8 );\n// returns ~-2.0557\n```\n\n#### Beta.prototype.mgf( t )\n\nEvaluates the [moment-generating function][mgf] (MGF).\n\n```javascript\nvar beta = new Beta( 2.0, 4.0 );\n\nvar y = beta.mgf( 0.5 );\n// returns ~1.186\n```\n\n#### Beta.prototype.pdf( x )\n\nEvaluates the [probability density function][pdf] (PDF).\n\n```javascript\nvar beta = new Beta( 2.0, 4.0 );\n\nvar y = beta.pdf( 0.8 );\n// returns ~0.128\n```\n\n#### Beta.prototype.quantile( p )\n\nEvaluates the [quantile function][quantile-function] at probability `p`.\n\n```javascript\nvar beta = new Beta( 2.0, 4.0 );\n\nvar y = beta.quantile( 0.5 );\n// returns ~0.314\n\ny = beta.quantile( 1.9 );\n// returns NaN\n```\n\n</section>\n\n<!-- /.usage -->\n\n<!-- Package 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<!-- Package usage examples. -->\n\n* * *\n\n<section class=\"examples\">\n\n## Examples\n\n<!-- eslint no-undef: \"error\" -->\n\n```javascript\nvar Beta = require( '@stdlib/stats-base-dists-beta-ctor' );\n\nvar beta = new Beta( 2.0, 4.0 );\n\nvar mu = beta.mean;\n// returns ~0.333\n\nvar median = beta.median;\n// returns ~0.314\n\nvar s2 = beta.variance;\n// returns ~0.032\n\nvar y = beta.cdf( 0.8 );\n// returns ~0.993\n```\n\n</section>\n\n<!-- /.examples -->\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-ctor.svg\n[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-beta-ctor\n\n[test-image]: https://github.com/stdlib-js/stats-base-dists-beta-ctor/actions/workflows/test.yml/badge.svg?branch=v0.2.3\n[test-url]: https://github.com/stdlib-js/stats-base-dists-beta-ctor/actions/workflows/test.yml?query=branch:v0.2.3\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-beta-ctor/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-beta-ctor?branch=main\n\n<!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/stats-base-dists-beta-ctor.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/stats-base-dists-beta-ctor/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-ctor/tree/deno\n[deno-readme]: https://github.com/stdlib-js/stats-base-dists-beta-ctor/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/stats-base-dists-beta-ctor/tree/umd\n[umd-readme]: https://github.com/stdlib-js/stats-base-dists-beta-ctor/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/stats-base-dists-beta-ctor/tree/esm\n[esm-readme]: https://github.com/stdlib-js/stats-base-dists-beta-ctor/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/stats-base-dists-beta-ctor/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-beta-ctor/main/LICENSE\n\n[beta-distribution]: https://en.wikipedia.org/wiki/Beta_distribution\n\n[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function\n\n[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function\n\n[pdf]: https://en.wikipedia.org/wiki/Probability_density_function\n\n[quantile-function]: https://en.wikipedia.org/wiki/Quantile_function\n\n[entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29\n\n[expected-value]: https://en.wikipedia.org/wiki/Expected_value\n\n[kurtosis]: https://en.wikipedia.org/wiki/Kurtosis\n\n[median]: https://en.wikipedia.org/wiki/Median\n\n[mode]: https://en.wikipedia.org/wiki/Mode_%28statistics%29\n\n[skewness]: https://en.wikipedia.org/wiki/Skewness\n\n[standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation\n\n[variance]: https://en.wikipedia.org/wiki/Variance\n\n</section>\n\n<!-- /.links -->\n","readmeFilename":"README.md"}