Quantile Function

Kumaraswamy's double bounded distribution quantile function.

The quantile function for a Kumaraswamy's double bounded random variable is

for 0 <= p <= 1, where a > 0 is the first shape parameter and b > 0 is the second shape parameter.

Installation

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

Usage

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

quantile( p, a, b )

Evaluates the quantile function for a Kumaraswamy's double bounded distribution with parameters a (first shape parameter) and b (second shape parameter).

var y = quantile( 0.5, 1.0, 1.0 );
// returns 0.5

y = quantile( 0.5, 2.0, 4.0 );
// returns ~0.399

y = quantile( 0.2, 2.0, 2.0 );
// returns ~0.325

y = quantile( 0.8, 4.0, 4.0 );
// returns ~0.759

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

var y = quantile( -0.5, 4.0, 2.0 );
// returns NaN

y = quantile( 1.5, 4.0, 2.0 );
// returns NaN

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

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

y = quantile( 0.2, NaN, 1.0 );
// returns NaN

y = quantile( 0.2, 1.0, NaN );
// returns NaN

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

var y = quantile( 0.2, -1.0, 0.5 );
// returns NaN

y = quantile( 0.2, 0.0, 0.5 );
// returns NaN

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

var y = quantile( 0.2, 0.5, -1.0 );
// returns NaN

y = quantile( 0.2, 0.5, 0.0 );
// returns NaN

quantile.factory( a, b )

Returns a function for evaluating the quantile function for a Kumaraswamy's double bounded distribution with parameters a (first shape parameter) and b (second shape parameter).

var myQuantile = quantile.factory( 0.5, 0.5 );

var y = myQuantile( 0.8 );
// returns ~0.922

y = myQuantile( 0.3 );
// returns ~0.26

Examples

var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var quantile = require( '@stdlib/stats-base-dists-kumaraswamy-quantile' );

var a;
var b;
var p;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    p = randu();
    a = ( randu()*5.0 ) + EPS;
    b = ( randu()*5.0 ) + EPS;
    y = quantile( p, a, b );
    console.log( 'p: %d, a: %d, b: %d, Q(p;a,b): %d', p.toFixed( 4 ), a.toFixed( 4 ), b.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.