Logarithm of Probability Density Function

Evaluate the natural logarithm of the probability density function (PDF) for an inverse gamma distribution.

The probability density function (PDF) for an inverse gamma random variable is

f left-parenthesis x semicolon alpha comma beta right-parenthesis equals StartFraction beta Superscript alpha Baseline Over normal upper Gamma left-parenthesis alpha right-parenthesis EndFraction x Superscript negative alpha minus 1 Baseline exp left-parenthesis minus StartFraction beta Over x EndFraction right-parenthesis

where alpha > 0 is the shape parameter and beta > 0 is the scale parameter.

Usage

var logpdf = require( '@stdlib/math/base/dists/invgamma/logpdf' );

logpdf( x, alpha, beta )

Evaluates the natural logarithm of the probability density function (PDF) for an inverse gamma distribution with parameters alpha (shape parameter) and beta (rate parameter).

var y = logpdf( 2.0, 0.5, 1.0 );
// returns ~-2.112

y = logpdf( 0.2, 1.0, 1.0 );
// returns ~-1.781

y = logpdf( -1.0, 4.0, 2.0 );
// returns -Infinity

If provided NaN as any argument, the function returns NaN.

var y = logpdf( NaN, 1.0, 1.0 );
// returns NaN

y = logpdf( 0.0, NaN, 1.0 );
// returns NaN

y = logpdf( 0.0, 1.0, NaN );
// returns NaN

If provided alpha <= 0, the function returns NaN.

var y = logpdf( 2.0, 0.0, 1.0 );
// returns NaN

y = logpdf( 2.0, -0.5, 1.0 );
// returns NaN

If provided beta <= 0, the function returns NaN.

var y = logpdf( 2.0, 1.0, 0.0 );
// returns NaN

y = logpdf( 2.0, 1.0, -1.0 );
// returns NaN

logpdf.factory( alpha, beta )

Returns a function for evaluating the natural logarithm of the PDF for an inverse gamma distribution with parameters alpha (shape parameter) and beta (rate parameter).

var mylogPDF = logpdf.factory( 6.0, 7.0 );

var y = mylogPDF( 2.0 );
// returns ~-1.464

Examples

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

var alpha;
var beta;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 2.0;
    alpha = randu() * 5.0;
    beta = randu() * 5.0;
    y = logpdf( x, alpha, beta );
    console.log( 'x: %d, α: %d, β: %d, ln(f(x;α,β)): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
}