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Quantile Function

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

[Kumaraswamy’s double bounded][kumaraswamy-distribution] distribution [quantile function][quantile].

The [quantile function][quantile] for a [Kumaraswamy’s double bounded][kumaraswamy-distribution] random variable is

math
Q(p;a,b) = \left( 1 - (1-p)^{\tfrac{1}{b}} \right)^{\tfrac{1}{a}}

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

## Installation

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

Alternatively,

- To load the package in a website via a script tag without installation and bundlers, use the [ES Module][es-module] available on the [esm][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [deno][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [umd][umd-url] branch (see [README][umd-readme]).

The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

## Usage

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

#### quantile( p, a, b )

Evaluates the [quantile function][quantile] for a [Kumaraswamy’s double bounded][kumaraswamy-distribution] distribution with parameters a (first shape parameter) and b (second shape parameter).

javascript
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.

javascript
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.

javascript
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.

javascript
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.

javascript
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][quantile] for a [Kumaraswamy’s double bounded][kumaraswamy-distribution] distribution with parameters a (first shape parameter) and b (second shape parameter).

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

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

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

## Examples

javascript
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][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][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

—-

## License

See [LICENSE][stdlib-license].

## Copyright

Copyright © 2016-2024. The Stdlib [Authors][stdlib-authors].