Cumulative Distribution Function

Gumbel distribution cumulative distribution function.

The cumulative distribution function for a Gumbel random variable is

upper F left-parenthesis x semicolon mu comma beta right-parenthesis equals e Superscript minus e Super Superscript minus left-parenthesis x minus mu right-parenthesis slash beta

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

Usage

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

cdf( x, mu, beta )

Evaluates the cumulative distribution function (CDF) for a Gumbel distribution with parameters mu (location parameter) and beta (scale parameter).

var y = cdf( 10.0, 0.0, 3.0 );
// returns ~0.965

y = cdf( -2.0, 0.0, 3.0 );
// returns ~0.143

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

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

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

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

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

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

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

y = cdf( 2.0, 0.0, 0.0 );
// returns NaN

cdf.factory( mu, beta )

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

var mycdf = cdf.factory( 0.0, 3.0 );

var y = mycdf( 10.0 );
// returns ~0.965

y = mycdf( -2.0 );
// returns ~0.143

Examples

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

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

for ( i = 0; i < 100; i++ ) {
    x = randu() * 10.0;
    mu = randu() * 10.0;
    beta = randu() * 10.0;
    y = cdf( x, mu, beta );
    console.log( 'x: %d, µ: %d, β: %d, F(x;µ,β): %d', x.toFixed( 4 ), mu.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
}