@stdlib/stats-base-dists-binomial-cdf
v0.2.3TypeScript
Binomial distribution cumulative distribution function (CDF).
0/weekUpdated yesterdayApache-2.0Unpacked: 58.2 KB
Published by The Stdlib Authors
npm install @stdlib/stats-base-dists-binomial-cdfWe 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!
About stdlib...
Cumulative Distribution Function
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> [Binomial][binomial-distribution] distribution [cumulative distribution function][cdf].
The [cumulative distribution function][cdf] for a [binomial][binomial-distribution] random variable is
where n is the number of trials and p is the success probability. The CDF can be equivalently expressed as
where I is the [lower regularized incomplete beta function][incomplete-beta].
Installation
``bash`
npm install @stdlib/stats-base-dists-binomial-cdf
Usage
`javascript`
var cdf = require( '@stdlib/stats-base-dists-binomial-cdf' );
#### cdf( x, n, p )
Evaluates the [cumulative distribution function][cdf] for a [binomial][binomial-distribution] distribution with number of trials n and success probability p.
`javascript
var y = cdf( 3.0, 20, 0.2 );
// returns ~0.411
y = cdf( 21.0, 20, 0.2 );
// returns 1.0
y = cdf( 5.0, 10, 0.4 );
// returns ~0.834
y = cdf( 0.0, 10, 0.4 );
// returns ~0.006
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = cdf( NaN, 20, 0.5 );
// returns NaN
y = cdf( 0.0, NaN, 0.5 );
// returns NaN
y = cdf( 0.0, 20, NaN );
// returns NaN
`
If provided a number of trials n which is not a nonnegative integer, the function returns NaN.
`javascript
var y = cdf( 2.0, 1.5, 0.5 );
// returns NaN
y = cdf( 2.0, -2.0, 0.5 );
// returns NaN
`
If provided a success probability p outside of [0,1], the function returns NaN.
`javascript
var y = cdf( 2.0, 20, -1.0 );
// returns NaN
y = cdf( 2.0, 20, 1.5 );
// returns NaN
`
#### cdf.factory( n, p )
Returns a function for evaluating the [cumulative distribution function][cdf] of a [binomial][binomial-distribution] distribution with number of trials n and success probability p.
`javascript
var mycdf = cdf.factory( 10, 0.5 );
var y = mycdf( 3.0 );
// returns ~0.172
y = mycdf( 1.0 );
// returns ~0.011
`
Examples
`javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var cdf = require( '@stdlib/stats-base-dists-binomial-cdf' );
var opts = {
'dtype': 'float64'
};
var x = uniform( 10, 0.0, 20.0, opts );
var n = discreteUniform( 10, 0, 100, opts );
var p = uniform( 10, 0.0, 1.0, opts );
logEachMap( 'x: %0.4f, n: %0.4f, p: %0.4f, F(x;n,p): %0.4f', x, n, p, cdf );
`
*
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
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-binomial-cdf.svg
[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-binomial-cdf
[test-image]: https://github.com/stdlib-js/stats-base-dists-binomial-cdf/actions/workflows/test.yml/badge.svg?branch=v0.2.3
[test-url]: https://github.com/stdlib-js/stats-base-dists-binomial-cdf/actions/workflows/test.yml?query=branch:v0.2.3
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-binomial-cdf/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-binomial-cdf?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-binomial-cdf/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-binomial-cdf/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-binomial-cdf/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-binomial-cdf/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-binomial-cdf/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-binomial-cdf/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-binomial-cdf/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-binomial-cdf/main/LICENSE
[binomial-distribution]: https://en.wikipedia.org/wiki/Binomial_distribution
[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
[incomplete-beta]: https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function