# @stdlib/stats-base-dists-kumaraswamy-quantile

0.2.1 • Public • Published

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# 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.

## Package Sidebar

### Install

`npm i @stdlib/stats-base-dists-kumaraswamy-quantile`

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