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!

Cumulative Distribution Function

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

> [Chi-squared][chisquare-distribution] distribution [cumulative distribution function][cdf].

The [cumulative distribution function][cdf] for a [chi-squared][chisquare-distribution] random variable is

Cumulative distribution function for a chi-squared distribution.

where k is the degrees of freedom and P is the lower regularized incomplete gamma function.

Installation

``bash npm install @stdlib/stats-base-dists-chisquare-cdf`

`Usage`

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

#### cdf( x, k )

Evaluates the [cumulative distribution function][cdf] (CDF) for a [chi-squared][chisquare-distribution] distribution with degrees of freedom k.

`javascript var y = cdf( 2.0, 1.0 ); // returns ~0.843

y = cdf( 2.0, 3.0 ); // returns ~0.428

y = cdf( 1.0, 0.5 ); // returns ~0.846

y = cdf( -1.0, 2.0 ); // returns 0.0

y = cdf( -Infinity, 4.0 ); // returns 0.0

y = cdf( +Infinity, 4.0 ); // returns 1.0`

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

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

y = cdf( 0.0, NaN ); // returns NaN`

If provided k < 0, the function returns NaN.

`javascript var y = cdf( 2.0, -2.0 ); // returns NaN`

If provided k = 0, the function evaluates the [CDF][cdf] of a [degenerate distribution][degenerate-distribution] centered at 0.

`javascript var y = cdf( 2.0, 0.0 ); // returns 1.0

y = cdf( -2.0, 0.0 ); // returns 0.0

y = cdf( 0.0, 0.0 ); // returns 1.0`

#### cdf.factory( k )

Returns a function for evaluating the [cumulative distribution function][cdf] for a [chi-squared][chisquare-distribution] distribution with degrees of freedom k.

`javascript var mycdf = cdf.factory( 3.0 );

var y = mycdf( 6.0 ); // returns ~0.888

y = mycdf( 1.5 ); // returns ~0.318`

*

`C APIs`

`$3`

`c #include "stdlib/stats/base/dists/chisquare/cdf.h"`

#### stdlib_base_dists_chisquare_cdf( x, k )

Evaluates the [cumulative distribution function][cdf] (CDF) for a [chi-squared][chisquare-distribution] distribution with degrees of freedom k.

`c double out = stdlib_base_dists_chisquare_cdf( 2.0, 1.0 ); // returns ~0.843

out = stdlib_base_dists_chisquare_cdf( 2.0, 3.0 ); // returns ~0.428`

The function accepts the following arguments:

- x: [in] doubleinput value. - k:[in] double degrees of freedom.

`c double stdlib_base_dists_chisquare_cdf( const double x, const double k );`

`$3`

`c #include "stdlib/stats/base/dists/chisquare/cdf.h" #include #include

static double random_uniform( double min, double max ) { double scale = rand() / (double) RAND_MAX; return min + ( scale * ( max - min ) ); }

int main( void ) { double x; double k; double y; int i;

for ( i = 0; i < 25; i++ ) { x = random_uniform( 0.0, 10.0 ); k = random_uniform( 1.0, 10.0 ); y = stdlib_base_dists_chisquare_cdf( x, k ); printf( "x: %lf, k: %lf, F(x;k): %lf\n", x, k, y ); } }`

*

`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-chisquare-cdf' );

var opts = { 'dtype': 'float64' }; var x = uniform( 20, 0.0, 10.0, opts ); var k = discreteUniform( 20, 0, 10, opts );

logEachMap( 'x: %0.4f, k: %d, F(x;k): %0.4f', x, k, 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`

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

[test-image]: https://github.com/stdlib-js/stats-base-dists-chisquare-cdf/actions/workflows/test.yml/badge.svg?branch=v0.3.1 [test-url]: https://github.com/stdlib-js/stats-base-dists-chisquare-cdf/actions/workflows/test.yml?query=branch:v0.3.1

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-chisquare-cdf/main.svg [coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-chisquare-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-chisquare-cdf/tree/deno [deno-readme]: https://github.com/stdlib-js/stats-base-dists-chisquare-cdf/blob/deno/README.md [umd-url]: https://github.com/stdlib-js/stats-base-dists-chisquare-cdf/tree/umd [umd-readme]: https://github.com/stdlib-js/stats-base-dists-chisquare-cdf/blob/umd/README.md [esm-url]: https://github.com/stdlib-js/stats-base-dists-chisquare-cdf/tree/esm [esm-readme]: https://github.com/stdlib-js/stats-base-dists-chisquare-cdf/blob/esm/README.md [branches-url]: https://github.com/stdlib-js/stats-base-dists-chisquare-cdf/blob/main/branches.md

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

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

[chisquare-distribution]: https://en.wikipedia.org/wiki/Chi-squared_distribution

[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution


  
    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!

`Cumulative Distribution Function`

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

> [Chi-squared][chisquare-distribution] distribution [cumulative distribution function][cdf].

The [cumulative distribution function][cdf] for a [chi-squared][chisquare-distribution] random variable is

where k is the degrees of freedom and P is the lower regularized incomplete gamma function.

`Installation`

``bash npm install @stdlib/stats-base-dists-chisquare-cdf `

`Usage`

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

#### cdf( x, k )

Evaluates the [cumulative distribution function][cdf] (CDF) for a [chi-squared][chisquare-distribution] distribution with degrees of freedom k.

`javascript var y = cdf( 2.0, 1.0 ); // returns ~0.843

y = cdf( 2.0, 3.0 ); // returns ~0.428

y = cdf( 1.0, 0.5 ); // returns ~0.846

y = cdf( -1.0, 2.0 ); // returns 0.0

y = cdf( -Infinity, 4.0 ); // returns 0.0

y = cdf( +Infinity, 4.0 ); // returns 1.0 `

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

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

y = cdf( 0.0, NaN ); // returns NaN `

If provided k < 0, the function returns NaN.

`javascript var y = cdf( 2.0, -2.0 ); // returns NaN `

If provided k = 0, the function evaluates the [CDF][cdf] of a [degenerate distribution][degenerate-distribution] centered at 0.

`javascript var y = cdf( 2.0, 0.0 ); // returns 1.0

y = cdf( -2.0, 0.0 ); // returns 0.0

y = cdf( 0.0, 0.0 ); // returns 1.0 `

#### cdf.factory( k )

Returns a function for evaluating the [cumulative distribution function][cdf] for a [chi-squared][chisquare-distribution] distribution with degrees of freedom k.

`javascript var mycdf = cdf.factory( 3.0 );

var y = mycdf( 6.0 ); // returns ~0.888

y = mycdf( 1.5 ); // returns ~0.318 `

*

`C APIs`

`$3`

`c #include "stdlib/stats/base/dists/chisquare/cdf.h" `

#### stdlib_base_dists_chisquare_cdf( x, k )

Evaluates the [cumulative distribution function][cdf] (CDF) for a [chi-squared][chisquare-distribution] distribution with degrees of freedom k.

`c double out = stdlib_base_dists_chisquare_cdf( 2.0, 1.0 ); // returns ~0.843

out = stdlib_base_dists_chisquare_cdf( 2.0, 3.0 ); // returns ~0.428 `

The function accepts the following arguments:

- x: [in] double input value. - k: [in] double degrees of freedom.

`c double stdlib_base_dists_chisquare_cdf( const double x, const double k ); `

`$3`

`c #include "stdlib/stats/base/dists/chisquare/cdf.h" #include #include

static double random_uniform( double min, double max ) { double scale = rand() / (double) RAND_MAX; return min + ( scale * ( max - min ) ); }

int main( void ) { double x; double k; double y; int i;

for ( i = 0; i < 25; i++ ) { x = random_uniform( 0.0, 10.0 ); k = random_uniform( 1.0, 10.0 ); y = stdlib_base_dists_chisquare_cdf( x, k ); printf( "x: %lf, k: %lf, F(x;k): %lf\n", x, k, y ); } } `

*

`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-chisquare-cdf' );

var opts = { 'dtype': 'float64' }; var x = uniform( 20, 0.0, 10.0, opts ); var k = discreteUniform( 20, 0, 10, opts );

logEachMap( 'x: %0.4f, k: %d, F(x;k): %0.4f', x, k, cdf ); `

*

`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-chisquare-cdf.svg [npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-chisquare-cdf

[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-chisquare-cdf/main/LICENSE

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

[chisquare-distribution]: https://en.wikipedia.org/wiki/Chi-squared_distribution

[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution