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

f left-parenthesis x semicolon k right-parenthesis equals StartFraction 2 Superscript 1 minus k slash 2 Baseline x Superscript k minus 1 Baseline e Superscript minus x squared slash 2 Baseline Over normal upper Gamma left-parenthesis k slash 2 right-parenthesis EndFraction

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

Usage

var logpdf = require( '@stdlib/math/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 ~-1.088

y = mylogPDF( 1.0 );
// returns ~-2.578

Examples

var randu = require( '@stdlib/random/base/randu' );
var logpdf = require( '@stdlib/math/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 ) );
}