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.

Installation

npm install @stdlib/stats-base-dists-gumbel-logpdf

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 );
}

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.