@stdlib/stats-base-dists-chisquare-logpdf
v0.2.2
Published
Natural logarithm of the probability density function (PDF) for a chi-squared distribution.
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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.
Community
License
See LICENSE.
Copyright
Copyright © 2016-2024. The Stdlib Authors.