Cumulative Distribution Function

Chi distribution cumulative distribution function.

The cumulative distribution function for a chi 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-chi-cdf

Usage

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

cdf( x, k )

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

var y = cdf( 2.0, 1.0 );
// returns ~0.954

y = cdf( 2.0, 3.0 );
// returns ~0.739

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 distribution with degrees of freedom k.

var mycdf = cdf.factory( 3.0 );

var y = mycdf( 6.0 );
// returns ~1.0

y = mycdf( 1.5 );
// returns ~0.478

Examples

var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var cdf = require( '@stdlib/stats-base-dists-chi-cdf' );

var k;
var x;
var y;
var i;

for ( i = 0; i < 20; i++ ) {
    x = randu() * 10.0;
    k = round( randu()*5.0 );
    y = cdf( x, k );
    console.log( 'x: %d, k: %d, F(x;k): %d', x.toFixed( 4 ), k.toFixed( 4 ), y.toFixed( 4 ) );
}

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 © 2016-2024. The Stdlib Authors.