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Chi-squared distribution cumulative distribution function (CDF).

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Apache-2.0 license

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Cumulative Distribution Function

Chi-squared distributioncumulative distribution function.

Thecumulative distribution function for achi-squared random variable is

$$F(x;\,k) = P\left(\frac{x}{2},\,\frac{k}{2}\right)$$

wherek is the degrees of freedom andP is the lower regularized incomplete gamma function.

Installation

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

Alternatively,

To load the package in a website via ascript tag without installation and bundlers, use theES Module available on theesm branch (seeREADME).
If you are using Deno, visit thedeno branch (seeREADME for usage intructions).
For use in Observable, or in browser/node environments, use theUniversal Module Definition (UMD) build available on theumd branch (seeREADME).

Thebranches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

varcdf=require('@stdlib/stats-base-dists-chisquare-cdf');

cdf( x, k )

Evaluates thecumulative distribution function (CDF) for achi-squared distribution with degrees of freedomk.

vary=cdf(2.0,1.0);// returns ~0.843y=cdf(2.0,3.0);// returns ~0.428y=cdf(1.0,0.5);// returns ~0.846y=cdf(-1.0,2.0);// returns 0.0y=cdf(-Infinity,4.0);// returns 0.0y=cdf(+Infinity,4.0);// returns 1.0

If providedNaN as any argument, the function returnsNaN.

vary=cdf(NaN,1.0);// returns NaNy=cdf(0.0,NaN);// returns NaN

If providedk < 0, the function returnsNaN.

vary=cdf(2.0,-2.0);// returns NaN

If providedk = 0, the function evaluates theCDF of adegenerate distribution centered at0.

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

cdf.factory( k )

Returns a function for evaluating thecumulative distribution function for achi-squared distribution with degrees of freedomk.

varmycdf=cdf.factory(3.0);vary=mycdf(6.0);// returns ~0.888y=mycdf(1.5);// returns ~0.318

C APIs

Usage

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

stdlib_base_dists_chisquare_cdf( x, k )

Evaluates thecumulative distribution function (CDF) for achi-squared distribution with degrees of freedomk.

doubleout=stdlib_base_dists_chisquare_cdf(2.0,1.0 );// returns ~0.843out=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.

doublestdlib_base_dists_chisquare_cdf(constdoublex,constdoublek );

Examples

#include"stdlib/stats/base/dists/chisquare/cdf.h"#include<stdlib.h>#include<stdio.h>staticdoublerandom_uniform(doublemin,doublemax ) {doublescale=rand() / (double)RAND_MAX;returnmin+ (scale* (max-min ) );}intmain(void ) {doublex;doublek;doubley;inti;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

vardiscreteUniform=require('@stdlib/random-array-discrete-uniform');varuniform=require('@stdlib/random-array-uniform');varlogEachMap=require('@stdlib/console-log-each-map');varcdf=require('@stdlib/stats-base-dists-chisquare-cdf');varopts={'dtype':'float64'};varx=uniform(20,0.0,10.0,opts);vark=discreteUniform(20,0,10,opts);logEachMap('x: %0.4f, k: %0.4f, F(x;k): %0.4f',x,k,cdf);

Notice

This package is part ofstdlib, 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 developstdlib, see the main projectrepository.