Logarithm of Probability Density Function

Gumbel distribution logarithm of probability density function (PDF).

The probability density function (PDF) for a Gumbel random variable is

f left-parenthesis x semicolon mu comma beta right-parenthesis equals StartFraction 1 Over beta EndFraction e Superscript minus left-parenthesis StartFraction x minus mu Over beta EndFraction plus e Super Superscript minus StartFraction x minus mu Over beta EndFraction Superscript right-parenthesis

where mu is the location parameter and beta > 0 is the scale parameter.

Usage

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

logpdf( x, mu, beta )

Evaluates the logarithm of the probability density function (PDF) for a Gumbel distribution with parameters mu (location parameter) and beta > 0 (scale parameter).

var y = logpdf( 0.0, 0.0, 2.0 );
// returns ~-1.693

y = logpdf( 0.0, 0.0, 1.0 );
// returns ~-1

y = logpdf( 1.0, 3.0, 2.0 );
// returns ~-2.408

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

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

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

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

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

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

y = logpdf( 2.0, 8.0, 0.0 );
// returns NaN

logpdf.factory( mu, beta )

Returns a function for evaluating the logarithm of the PDF (PDF) for a Gumbel distribution with parameters mu (location parameter) and beta > 0 (scale parameter).

var mylogpdf = logpdf.factory( 10.0, 2.0 );

y = mylogpdf( 10.0 );
// returns ~-1.693

y = mylogpdf( 12.0 );
// returns ~-2.064

Examples

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

var beta;
var mu;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 10.0;
    mu = randu() * 10.0;
    beta = randu() * 10.0;
    y = logpdf( x, mu, beta );
    console.log( 'x: %d, µ: %d, β: %d, ln(f(x;µ,β)): %d', x, mu, beta, y );
}