Quantile Function

Fréchet distribution quantile function.

The quantile function for a Fréchet random variable is

upper Q left-parenthesis p semicolon alpha comma s comma m right-parenthesis equals m plus s left-parenthesis minus ln p right-parenthesis Superscript minus StartFraction 1 Over alpha EndFraction

where alpha > 0 is the shape, s > 0 the scale, and m the location parameter.

Usage

var quantile = require( '@stdlib/math/base/dists/frechet/quantile' );

quantile( x, alpha, s, m )

Evaluates the quantile function for a Fréchet distribution with shape alpha, scale s, and location m at a probability p.

var y = quantile( 0.8, 2.0, 3.0, 5.0 );
// returns ~11.351

y = quantile( 0.1, 1.0, 2.0, -4.0 );
// returns ~-3.131

y = quantile( 0.3, 2.0, 1.0, -1.0 );
// returns ~-0.089

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

var y = quantile( 1.9, 2.0, 2.0, 0.0 );
// returns NaN

y = quantile( -0.1, 2.0, 2.0, 0.0 );
// returns NaN

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

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

y = quantile( 0.9, NaN, 1.0, 0.0 );
// returns NaN

y = quantile( 0.9, 1.0, NaN, 0.0);
// returns NaN

y = quantile( 0.9, 1.0, 1.0, NaN );
// returns NaN

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

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

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

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

var y = quantile( 0.3, 1.0, -1.0, 1.0 );
// returns NaN

y = quantile( 0.3, 1.0, 0.0, 1.0 );
// returns NaN

quantile function.factory( alpha, s, m )

Returns a function for evaluating the quantile function of a Fréchet distribution with shape alpha, scale s, and location m.

var myQuantile = quantile.factory( 3.0, 3.0, 5.0 );

var y = myQuantile( 10.0 );
// returns ~0.806

y = myQuantile( 7.0 );
// returns ~0.034

Examples

var randu = require( '@stdlib/random/base/randu' );
var quantile = require( '@stdlib/math/base/dists/frechet/quantile' );

var alpha;
var m;
var s;
var p;
var y;
var i;

for ( i = 0; i < 100; i++ ) {
    alpha = randu() * 10.0;
    p = randu();
    s = randu() * 10.0;
    m = randu() * 10.0;
    y = quantile( p, alpha, s, m );
    console.log( 'x: %d, α: %d, s: %d, m: %d, Q(p;α,s,m): %d', p.toFixed( 4 ), alpha.toFixed( 4 ), s.toFixed( 4 ), m.toFixed( 4 ), y.toFixed( 4 ) );
}