Logarithm of Probability Density Function

Gumbel distribution logarithm of probability density function (PDF).

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

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

Usage

var logpdf = require( '@stdlib/stats/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 ~-2.411

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 ~-2.061

Notes

In virtually all cases, using the logpdf or logcdf functions is preferable to manually computing the logarithm of the pdf or cdf, respectively, since the latter is prone to overflow and underflow.

Examples

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