# npm

## @stdlib/stats-base-dists-chisquare-logpdf

0.0.7 • Public • Published

# Logarithm of Probability Density Function

Evaluate the natural logarithm of the probability density function (PDF) for a chi-squared distribution.

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-logpdf

## Usage

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

#### logpdf( x, k )

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

var y = logpdf( 0.1, 1.0 );
// returns ~0.182

y = logpdf( 0.5, 2.0 );
// returns ~-0.943

y = logpdf( -1.0, 4.0 );
// returns -Infinity

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

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

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

If provided k < 0, the function returns NaN.

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

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

var y = logpdf( 2.0, 0.0 );
// returns -Infinity

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

#### logpdf.factory( k )

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

var myLogPDF = logpdf.factory( 6.0 );

var y = myLogPDF( 3.0 );
// returns ~-2.075

y = myLogPDF( 1.0 );
// returns ~-3.273

## Examples

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

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

for ( i = 0; i < 20; i++ ) {
x = randu() * 10.0;
k = randu() * 10.0;
y = logpdf( x, k );
console.log( 'x: %d, k: %d, ln(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.

### Install

npm i @stdlib/stats-base-dists-chisquare-logpdf

stdlib.io

102

0.0.7

Apache-2.0

38.2 kB

11