Probability Density Function

Gumbel distribution 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-pdf

Usage

var pdf = require( '@stdlib/stats-base-dists-gumbel-pdf' );

pdf( x, mu, beta )

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

var y = pdf( 0.0, 0.0, 2.0 );
// returns ~0.184

y = pdf( 0.0, 0.0, 1.0 );
// returns ~0.368

y = pdf( 1.0, 3.0, 2.0 );
// returns ~0.09

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

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

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

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

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

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

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

pdf.factory( mu, beta )

Partially apply mu and beta to create a reusable function for evaluating the PDF.

var mypdf = pdf.factory( 10.0, 2.0 );

y = mypdf( 10.0 );
// returns ~0.184

y = mypdf( 12.0 );
// returns ~0.127

Examples

var randu = require( '@stdlib/random-base-randu' );
var pdf = require( '@stdlib/stats-base-dists-gumbel-pdf' );

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 = pdf( x, mu, beta );
    console.log( 'x: %d, µ: %d, β: %d, 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.