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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.
npm install @stdlib/stats-base-dists-chi-logpdf
Alternatively,
- To load the package in a website via a
script
tag without installation and bundlers, use the ES Module available on theesm
branch (see README). - If you are using Deno, visit the
deno
branch (see README for usage intructions). - For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the
umd
branch (see README).
The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.
To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
var logpdf = require( '@stdlib/stats-base-dists-chi-logpdf' );
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
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
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 ) );
}
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.
See LICENSE.
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