Quantile Function

Gumbel distribution quantile function.

The quantile function for a Gumbel random variable is

for 0 <= p < 1, where mu is the location parameter and beta > 0 is the scale parameter.

Installation

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

Usage

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

quantile( p, mu, beta )

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

var y = quantile( 0.8, 0.0, 1.0 );
// returns ~1.5

y = quantile( 0.5, 4.0, 2.0 );
// returns ~4.733

y = quantile( 0.5, 4.0, 4.0 );
// returns ~5.466

If provided a probability p outside the interval [0,1], the function returns NaN.

var y = quantile( 1.9, 0.0, 1.0 );
// returns NaN

y = quantile( -0.1, 0.0, 1.0 );
// returns NaN

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

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

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

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

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

var y = quantile( 0.4, 0.0, -1.0 );
// returns NaN

y = quantile( 0.4, 0.0, 0.0 );
// returns NaN

quantile.factory( mu, beta )

Returns a function for evaluating the quantile function of a Gumbel distribution with parameters mu and beta.

var myquantile = quantile.factory( 10.0, 2.0 );

var y = myquantile( 0.2 );
// returns ~9.048

y = myquantile( 0.8 );
// returns ~13.00

Examples

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

var beta;
var mu;
var p;
var y;
var i;

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

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.