# 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.

## Usage

var logpdf = require( '@stdlib/math/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 ~-2.071

y = myLogPDF( 1.0 );
// returns ~-1.959


## Examples

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