Quantile Function

Gumbel distribution quantile function.

The quantile function for a Gumbel random variable is

upper Q left-parenthesis p right-parenthesis equals mu minus beta ln left-parenthesis minus ln left-parenthesis p right-parenthesis right-parenthesis

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

Usage

var quantile = require( '@stdlib/math/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/math/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 ) );
}