Probability Density Function

Chi-squared distribution probability density function (PDF).

The probability density function (PDF) for a chi-squared random variable is

where k is the degrees of freedom and Γ denotes the gamma function.

Installation

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

Usage

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

pdf( x, k )

Evaluates the probability density function (PDF) for a chi-squared distribution with degrees of freedom k.

var y = pdf( 0.1, 1.0 );
// returns ~1.2

y = pdf( 0.5, 2.0 );
// returns ~0.389

y = pdf( -1.0, 4.0 );
// returns 0.0

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

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

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

If provided k < 0, the function returns NaN.

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

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

var y = pdf( 2.0, 0.0 );
// returns 0.0

y = pdf( 0.0, 0.0 );
// returns Infinity

pdf.factory( k )

Returns a function for evaluating the PDF for a chi-squared distribution with degrees of freedom k.

var myPDF = pdf.factory( 6.0 );

var y = myPDF( 3.0 );
// returns ~0.126

y = myPDF( 1.0 );
// returns ~0.038

Examples

var randu = require( '@stdlib/random-base-randu' );
var pdf = require( '@stdlib/stats-base-dists-chisquare-pdf' );

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

for ( i = 0; i < 20; i++ ) {
    x = randu() * 10.0;
    k = randu() * 10.0;
    y = pdf( 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.