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

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

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

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

Examples

var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var pdf = require( '@stdlib/stats-base-dists-gumbel-pdf' );

var opts = {
    'dtype': 'float64'
};
var beta = uniform( 100, 0.0, 10.0, opts );
var mu = uniform( 100, 0.0, 10.0, opts );
var x = uniform( 100, 0.0, 10.0, opts );

logEachMap( 'x: %0.4f, µ: %0.4f, β: %0.4f, f(x;µ,β): %0.4f', x, mu, beta, pdf );

C APIs

Usage

#include "stdlib/stats/base/dists/gumbel/pdf.h"

stdlib_base_dists_gumbel_pdf( x, mu, beta )

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

double out = stdlib_base_dists_gumbel_pdf( 0.0, 0.0, 2.0 );
// returns ~0.184

The function accepts the following arguments:

• x: [in] double input value.
• mu: [in] double location parameter.
• beta: [in] double scale parameter.

double stdlib_base_dists_gumbel_pdf( const double x, const double mu, const double beta );

Examples

#include "stdlib/stats/base/dists/gumbel/pdf.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double beta;
    double mu;
    double x;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x = random_uniform( 0.0, 10.0 );
        mu = random_uniform( 0.0, 10.0 );
        beta = random_uniform( 0.0, 10.0 );
        y = stdlib_base_dists_gumbel_pdf( x, mu, beta );
        printf( "x: %lf, µ: %lf, β: %lf, f(x;µ,β): %lf\n", 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 © 2016-2026. The Stdlib Authors.