npm package: @stdlib/stats-base-dists-betaprime-quantile
Description: Beta prime distribution quantile function.
Author: The Stdlib Authors
Latest version: 0.2.3

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# Quantile Function

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

> [Beta prime][betaprime-distribution] distribution [quantile function][quantile-function].

<section class="intro">

The [quantile function][quantile-function] for a [beta prime][betaprime-distribution] random variable with first shape parameter `α > 0` and second shape parameter `β > 0` is

<!-- <equation class="equation" label="eq:betaprime_quantile_function" align="center" raw="Q(p;\alpha,\beta)\,= \frac{G^{-1}(p)}{1-G^{-1}(p)}" alt="Quantile function for a beta prime distribution."> -->

<div class="equation" align="center" data-raw-text="Q(p;\alpha,\beta)\,= \frac{G^{-1}(p)}{1-G^{-1}(p)}" data-equation="eq:betaprime_quantile_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/betaprime/quantile/docs/img/equation_betaprime_quantile_function.svg" alt="Quantile function for a beta prime distribution.">
    <br>
</div>

<!-- </equation> -->

for `0 <= p <= 1`, where `G^-1` denotes the quantile function of a [beta][beta-distribution] random variable with parameters `α` and `β`.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-betaprime-quantile
```

</section>

<section class="usage">

## Usage

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

#### quantile( p, alpha, beta )

Evaluates the [quantile function][quantile-function] for a [beta prime][betaprime-distribution] distribution with parameters `alpha` (first shape parameter) and `beta` (second shape parameter).

```javascript
var y = quantile( 0.8, 2.0, 1.0 );
// returns ~8.472

y = quantile( 0.5, 4.0, 2.0 );
// returns ~2.187
```

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

```javascript
var y = quantile( 1.9, 1.0, 1.0 );
// returns NaN

y = quantile( -0.1, 1.0, 1.0 );
// 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( 0.5, NaN, 1.0 );
// returns NaN

y = quantile( 0.5, 1.0, NaN );
// returns NaN
```

If provided `alpha <= 0`, the function returns `NaN`.

```javascript
var y = quantile( 0.4, -1.0, 1.0 );
// returns NaN

y = quantile( 0.4, 0.0, 1.0 );
// returns NaN
```

If provided `beta <= 0`, the function returns `NaN`.

```javascript
var y = quantile( 0.4, 1.0, -1.0 );
// returns NaN

y = quantile( 0.4, 1.0, 0.0 );
// returns NaN
```

#### quantile.factory( alpha, beta )

Returns a function for evaluating the [quantile function][quantile-function] of a [beta prime][betaprime-distribution] distribution with parameters `alpha` (first shape parameter) and `beta` (second shape parameter).

```javascript
var myQuantile = quantile.factory( 2.0, 2.0 );

var y = myQuantile( 0.8 );
// returns ~2.483

y = myQuantile( 0.4 );
// returns ~0.763
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var EPS = require( '@stdlib/constants-float64-eps' );
var quantile = require( '@stdlib/stats-base-dists-betaprime-quantile' );

var opts = {
    'dtype': 'float64'
};
var alpha = uniform( 10, EPS, 5.0, opts );
var beta = uniform( 10, EPS, 5.0, opts );
var p = uniform( 10, 0.0, 1.0, opts );

logEachMap( 'p: %0.4f, α: %0.4f, β: %0.4f, Q(p;α,β): %0.4f', p, alpha, beta, quantile );
```

</section>

<!-- /.examples -->

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

<section class="related">

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## 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

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[beta-distribution]: https://en.wikipedia.org/wiki/Beta_distribution

[betaprime-distribution]: https://en.wikipedia.org/wiki/Beta_prime_distribution

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

</section>

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