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

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

Chi-squared distribution cumulative distribution function.

The cumulative distribution function for a chi-squared random variable is

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

Installation

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

Usage

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

cdf( x, k )

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

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.

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

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

If provided k < 0, the function returns NaN.

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

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

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 for a chi-squared distribution with degrees of freedom k.

var mycdf = cdf.factory( 3.0 );

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

y = 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 the cumulative distribution function (CDF) for a chi-squared distribution with degrees of freedom k.

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.

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

Examples

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

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

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, 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, see the main project repository.

Community

---

License

See LICENSE.

Copyright

Copyright 2016-2026. The Stdlib Authors.