npm package: @stdlib/stats-base-dists-bradford-quantile
Description: Bradford distribution quantile function.
Author: The Stdlib Authors
Latest version: 0.1.1

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</details>

# 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] -->

> [Bradford][bradford-distribution] distribution [quantile function][quantile-function].

<section class="intro">

The [quantile function][quantile-function] for a [Bradford][bradford-distribution] random variable is

<!-- <equation class="equation" label="eq:bradford_quantile_function" align="center" raw="Q(p;c)=\frac{(1+c)^p - 1}{c}" alt="Quantile function for a Bradford distribution."> -->

<div class="equation" align="center" data-raw-text="Q(p;c)=\frac{(1+c)^p - 1}{c}" data-equation="eq:bradford_quantile_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/bradford/quantile/docs/img/equation_bradford_quantile_function.svg" alt="Quantile function for a Bradford distribution.">
    <br>
</div>

<!-- </equation> -->

for `0 <= p <= 1`, where `c` is the shape parameter.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### quantile( p, c )

Evaluates the [quantile function][quantile-function] for a [Bradford][bradford-distribution] distribution with shape parameter `c` at a probability `p`.

```javascript
var y = quantile( 0.1, 0.1 );
// returns ~0.096

y = quantile( 0.5, 5.0 );
// returns ~0.290

y = quantile( 1.0, 10.0 );
// returns 1.0
```

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

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

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

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

```javascript
var y = quantile( 2.0, 0.5 );
// returns NaN

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

If provided a shape parameter `c <= 0`, the function returns `NaN`.

```javascript
var y = quantile( 0.5, 0.0 );
// returns NaN

y = quantile( 0.5, -10.0 );
// returns NaN
```

#### quantile.factory( c )

Returns a function for evaluating the [quantile function][quantile-function] for a [Bradford][bradford-distribution] distribution with shape parameter `c`.

```javascript
var myquantile = quantile.factory( 5.0 );
var y = myquantile( 0.4 );
// returns ~0.210

y = myquantile( 0.8 );
// returns ~0.639

y = myquantile( 1.0 );
// returns 1.0
```

</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 quantile = require( '@stdlib/stats-base-dists-bradford-quantile' );

var opts = {
    'dtype': 'float64'
};
var p = uniform( 10, 0.0, 1.0, opts );
var c = uniform( 10, 0.1, 10.0, opts );

logEachMap( 'p: %0.4f, c: %0.4f, Q(p;c): %0.4f', p, c, quantile );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

<section class="c">

## C APIs

<section class="intro">

</section>

<!-- /.intro -->

<section class="usage">

### Usage

```c
#include "stdlib/stats/base/dists/bradford/quantile.h"
```

#### stdlib_base_dists_bradford_quantile( p, c )

Returns the quantile function of a Bradford distribution.

```c
double out = stdlib_base_dists_bradford_quantile( 0.5, 5.0 );
// returns ~0.290
```

The function accepts the following arguments:

-   **p**: `[in] double` input probability.
-   **c**: `[in] double` shape parameter.

```c
double stdlib_base_dists_bradford_quantile( const double p, const double c );
```

</section>

<!-- /.usage -->

<section class="notes">

</section>

<!-- /.notes -->

<section class="examples">

### Examples

```c
#include "stdlib/stats/base/dists/bradford/quantile.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double p;
    double c;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        p = random_uniform( 0.0, 1.0 );
        c = random_uniform( 0.01, 10.0 );
        y = stdlib_base_dists_bradford_quantile( p, c );
        printf( "p: %lf, c: %lf, Q(p;c): %lf\n", p, c, y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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<section class="related">

</section>

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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].

</section>

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[bradford-distribution]: https://en.wikipedia.org/wiki/Bradford%27s_law

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

</section>

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