Logarithm of Probability Density Function

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

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

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

Installation

npm install @stdlib/stats-base-dists-chi-logpdf

Usage

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

logpdf( x, k )

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

var y = logpdf( 0.1, 1.0 );
// returns ~-0.231

y = logpdf( 0.5, 2.0 );
// returns ~-0.818

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 natural logarithm of the PDF for 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 natural logarithm of the PDF for a chi distribution with degrees of freedom k.

var mylogPDF = logpdf.factory( 6.0 );

var y = mylogPDF( 3.0 );
// returns ~-1.086

y = mylogPDF( 1.0 );
// returns ~-2.579

Examples

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

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.