Quantile Function

Fréchet distribution quantile function.

The quantile function for a Fréchet random variable is

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

Installation

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

Usage

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

quantile( p, 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.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( 0.7 );
// returns ~9.23

y = myQuantile( 0.2 );
// returns ~7.56

Examples

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

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.