@stdlib/stats/base/dists/kumaraswamy/quantile/README.md

Standard library statistical functions.

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# Quantile Function

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

<section class="intro">

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

<!-- <equation class="equation" label="eq:beta_quantile_function" align="center" raw="Q(p;a,b) = \left( 1 - (1-p)^{\tfrac{1}{b}} \right)^{\tfrac{1}{a}}" alt="Quantile function for a Kumaraswamy's double bounded distribution."> -->

<div class="equation" align="center" data-raw-text="Q(p;a,b) = \left( 1 - (1-p)^{\tfrac{1}{b}} \right)^{\tfrac{1}{a}}" data-equation="eq:beta_quantile_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/quantile/docs/img/equation_beta_quantile_function.svg" alt="Quantile function for a Kumaraswamy's double bounded distribution.">
    <br>
</div>

<!-- </equation> -->

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

</section>

<!-- /.intro -->

<section class="usage">

## 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
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```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 ) );
}
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="links">

[kumaraswamy-distribution]: https://en.wikipedia.org/wiki/Kumaraswamy_distribution

[quantile]: https://en.wikipedia.org/wiki/Quantile_function

</section>

<!-- /.links -->