About stdlib...

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.

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.

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.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

Logarithm of Cumulative Distribution Function

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

> [Beta][beta-distribution] distribution logarithm of [cumulative distribution function][cdf].

The [cumulative distribution function][cdf] for a [beta][beta-distribution] random variable is

Cumulative distribution function for a beta distribution.

where alpha > 0 is the first shape parameter and beta > 0 is the second shape parameter. In the definition, Beta( x; a, b ) denotes the lower incomplete beta function and Beta( a, b ) the [beta function][beta-function].

Installation

``bash npm install @stdlib/stats-base-dists-beta-logcdf`

`Usage`

`javascript var logcdf = require( '@stdlib/stats-base-dists-beta-logcdf' );`

#### logcdf( x, alpha, beta )

Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF) for a [beta][beta-distribution] distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

`javascript var y = logcdf( 0.5, 1.0, 1.0 ); // returns ~-0.693

y = logcdf( 0.5, 2.0, 4.0 ); // returns ~-0.208

y = logcdf( 0.2, 2.0, 2.0 ); // returns ~-2.263

y = logcdf( 0.8, 4.0, 4.0 ); // returns ~-0.034

y = logcdf( -0.5, 4.0, 2.0 ); // returns -Infinity

y = logcdf( -Infinity, 4.0, 2.0 ); // returns -Infinity

y = logcdf( 1.5, 4.0, 2.0 ); // returns 0.0

y = logcdf( +Infinity, 4.0, 2.0 ); // returns 0.0`

If provided NaN as any argument, the function returns NaN.

`javascript var y = logcdf( NaN, 1.0, 1.0 ); // returns NaN

y = logcdf( 0.0, NaN, 1.0 ); // returns NaN

y = logcdf( 0.0, 1.0, NaN ); // returns NaN`

If provided alpha <= 0, the function returns NaN.

`javascript var y = logcdf( 2.0, -1.0, 0.5 ); // returns NaN

y = logcdf( 2.0, 0.0, 0.5 ); // returns NaN`

If provided beta <= 0, the function returns NaN.

`javascript var y = logcdf( 2.0, 0.5, -1.0 ); // returns NaN

y = logcdf( 2.0, 0.5, 0.0 ); // returns NaN`

#### logcdf.factory( alpha, beta )

Returns a function for evaluating the natural logarithm of the [cumulative distribution function][cdf] for a [beta][beta-distribution] distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

`javascript var mylogcdf = logcdf.factory( 0.5, 0.5 );

var y = mylogcdf( 0.8 ); // returns ~-0.35

y = mylogcdf( 0.3 ); // returns ~-0.997`

`Notes`

- 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.

`Examples`

`javascript var uniform = require( '@stdlib/random-array-uniform' ); var logEachMap = require( '@stdlib/console-log-each-map' ); var EPS = require( '@stdlib/constants-float64-eps' ); var logcdf = require( '@stdlib/stats-base-dists-beta-logcdf' );

var opts = { 'dtype': 'float64' }; var alpha = uniform( 10, EPS, 10.0, opts ); var beta = uniform( 10, EPS, 10.0, opts ); var x = uniform( 10, 0.0, 1.0, opts );

logEachMap( 'x: %0.4f, α: %0.4f, β: %0.4f, ln(F(x;α,β)): %0.4f', x, alpha, beta, logcdf );`

*

`Notice`

This 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.

For 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].

#### Community

[![Chat][chat-image]][chat-url]

---

`License`

See [LICENSE][stdlib-license].

`Copyright`

[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-beta-logcdf.svg [npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-beta-logcdf

[test-image]: https://github.com/stdlib-js/stats-base-dists-beta-logcdf/actions/workflows/test.yml/badge.svg?branch=v0.2.3 [test-url]: https://github.com/stdlib-js/stats-base-dists-beta-logcdf/actions/workflows/test.yml?query=branch:v0.2.3

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-beta-logcdf/main.svg [coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-beta-logcdf?branch=main

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com

[stdlib]: https://github.com/stdlib-js/stdlib

[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors

[umd]: https://github.com/umdjs/umd [es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[deno-url]: https://github.com/stdlib-js/stats-base-dists-beta-logcdf/tree/deno [deno-readme]: https://github.com/stdlib-js/stats-base-dists-beta-logcdf/blob/deno/README.md [umd-url]: https://github.com/stdlib-js/stats-base-dists-beta-logcdf/tree/umd [umd-readme]: https://github.com/stdlib-js/stats-base-dists-beta-logcdf/blob/umd/README.md [esm-url]: https://github.com/stdlib-js/stats-base-dists-beta-logcdf/tree/esm [esm-readme]: https://github.com/stdlib-js/stats-base-dists-beta-logcdf/blob/esm/README.md [branches-url]: https://github.com/stdlib-js/stats-base-dists-beta-logcdf/blob/main/branches.md

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-beta-logcdf/main/LICENSE

[beta-distribution]: https://en.wikipedia.org/wiki/Beta_distribution

[beta-function]: https://en.wikipedia.org/wiki/Beta_function

[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function


  
    About stdlib...
  

  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.

  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.

  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.

  To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

`Logarithm of Cumulative Distribution Function`

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

> [Beta][beta-distribution] distribution logarithm of [cumulative distribution function][cdf].

The [cumulative distribution function][cdf] for a [beta][beta-distribution] random variable is

where alpha > 0 is the first shape parameter and beta > 0 is the second shape parameter. In the definition, Beta( x; a, b ) denotes the lower incomplete beta function and Beta( a, b ) the [beta function][beta-function].

`Installation`

``bash npm install @stdlib/stats-base-dists-beta-logcdf `

`Usage`

`javascript var logcdf = require( '@stdlib/stats-base-dists-beta-logcdf' ); `

#### logcdf( x, alpha, beta )

Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF) for a [beta][beta-distribution] distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

`javascript var y = logcdf( 0.5, 1.0, 1.0 ); // returns ~-0.693

y = logcdf( 0.5, 2.0, 4.0 ); // returns ~-0.208

y = logcdf( 0.2, 2.0, 2.0 ); // returns ~-2.263

y = logcdf( 0.8, 4.0, 4.0 ); // returns ~-0.034

y = logcdf( -0.5, 4.0, 2.0 ); // returns -Infinity

y = logcdf( -Infinity, 4.0, 2.0 ); // returns -Infinity

y = logcdf( 1.5, 4.0, 2.0 ); // returns 0.0

y = logcdf( +Infinity, 4.0, 2.0 ); // returns 0.0 `

If provided NaN as any argument, the function returns NaN.

`javascript var y = logcdf( NaN, 1.0, 1.0 ); // returns NaN

y = logcdf( 0.0, NaN, 1.0 ); // returns NaN

y = logcdf( 0.0, 1.0, NaN ); // returns NaN `

If provided alpha <= 0, the function returns NaN.

`javascript var y = logcdf( 2.0, -1.0, 0.5 ); // returns NaN

y = logcdf( 2.0, 0.0, 0.5 ); // returns NaN `

If provided beta <= 0, the function returns NaN.

`javascript var y = logcdf( 2.0, 0.5, -1.0 ); // returns NaN

y = logcdf( 2.0, 0.5, 0.0 ); // returns NaN `

#### logcdf.factory( alpha, beta )

Returns a function for evaluating the natural logarithm of the [cumulative distribution function][cdf] for a [beta][beta-distribution] distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

`javascript var mylogcdf = logcdf.factory( 0.5, 0.5 );

var y = mylogcdf( 0.8 ); // returns ~-0.35

y = mylogcdf( 0.3 ); // returns ~-0.997 `

`Notes`

- 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.

`Examples`

`javascript var uniform = require( '@stdlib/random-array-uniform' ); var logEachMap = require( '@stdlib/console-log-each-map' ); var EPS = require( '@stdlib/constants-float64-eps' ); var logcdf = require( '@stdlib/stats-base-dists-beta-logcdf' );

var opts = { 'dtype': 'float64' }; var alpha = uniform( 10, EPS, 10.0, opts ); var beta = uniform( 10, EPS, 10.0, opts ); var x = uniform( 10, 0.0, 1.0, opts );

logEachMap( 'x: %0.4f, α: %0.4f, β: %0.4f, ln(F(x;α,β)): %0.4f', x, alpha, beta, logcdf ); `

*

`Notice`

For 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].

#### Community

[![Chat][chat-image]][chat-url]

---

`License`

See [LICENSE][stdlib-license].

`Copyright`

[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-beta-logcdf.svg [npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-beta-logcdf

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com

[stdlib]: https://github.com/stdlib-js/stdlib

[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors

[umd]: https://github.com/umdjs/umd [es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-beta-logcdf/main/LICENSE

[beta-distribution]: https://en.wikipedia.org/wiki/Beta_distribution

[beta-function]: https://en.wikipedia.org/wiki/Beta_function

[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function