npm package: @stdlib/stats-base-dists-frechet-quantile
Description: Fréchet distribution quantile function.
Author: The Stdlib Authors
Latest version: 0.3.1

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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] -->

> [Fréchet][frechet-distribution] distribution [quantile function][quantile].

<section class="intro">

The [quantile function][quantile] for a [Fréchet][frechet-distribution] random variable is

<!-- <equation class="equation" label="eq:frechet_quantile" align="center" raw="Q\left( p; \alpha, s, m \right ) = m + s ( -\ln p )^{-\tfrac{1}{\alpha}}" alt="Quantile function for a Fréchet distribution."> -->

<div class="equation" align="center" data-raw-text="Q\left( p; \alpha, s, m \right ) = m + s ( -\ln p )^{-\tfrac{1}{\alpha}}" data-equation="eq:frechet_quantile">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/frechet/quantile/docs/img/equation_frechet_quantile.svg" alt="Quantile function for a Fréchet distribution.">
    <br>
</div>

<!-- </equation> -->

where `alpha > 0` is the shape, `s > 0` the scale, and `m` the location parameter.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### quantile( p, alpha, s, m )

Evaluates the [quantile function][quantile] for a [Fréchet][frechet-distribution] distribution with shape `alpha`, scale `s`, and location `m` at a probability `p`.

```javascript
var y = quantile( 0.8, 2.0, 3.0, 5.0 );
// returns ~11.351

y = quantile( 0.1, 1.0, 2.0, -4.0 );
// returns ~-3.131

y = quantile( 0.3, 2.0, 1.0, -1.0 );
// returns ~-0.089
```

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

```javascript
var y = quantile( 1.9, 2.0, 2.0, 0.0 );
// returns NaN

y = quantile( -0.1, 2.0, 2.0, 0.0 );
// returns NaN
```

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

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

y = quantile( 0.9, NaN, 1.0, 0.0 );
// returns NaN

y = quantile( 0.9, 1.0, NaN, 0.0);
// returns NaN

y = quantile( 0.9, 1.0, 1.0, NaN );
// returns NaN
```

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

```javascript
var y = quantile( 0.1, -0.1, 1.0, 1.0 );
// returns NaN

y = quantile( 0.1, 0.0, 1.0, 1.0 );
// returns NaN
```

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

```javascript
var y = quantile( 0.3, 1.0, -1.0, 1.0 );
// returns NaN

y = quantile( 0.3, 1.0, 0.0, 1.0 );
// returns NaN
```

#### quantile.factory( alpha, s, m )

Returns a function for evaluating the [quantile function][quantile] of a [Fréchet][frechet-distribution] distribution with shape `alpha`, scale `s`, and location `m`.

```javascript
var myQuantile = quantile.factory( 3.0, 3.0, 5.0 );

var y = myQuantile( 0.7 );
// returns ~9.23

y = myQuantile( 0.2 );
// returns ~7.56
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

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

var alpha;
var m;
var s;
var p;
var y;
var i;

for ( i = 0; i < 100; i++ ) {
    alpha = randu() * 10.0;
    p = randu();
    s = randu() * 10.0;
    m = randu() * 10.0;
    y = quantile( p, alpha, s, m );
    console.log( 'x: %d, α: %d, s: %d, m: %d, Q(p;α,s,m): %d', p.toFixed( 4 ), alpha.toFixed( 4 ), s.toFixed( 4 ), m.toFixed( 4 ), y.toFixed( 4 ) );
}
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

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

#### stdlib_base_dists_frechet_quantile( p, alpha, s, m )

Evaluates the [quantile function][quantile] for a [Fréchet][frechet-distribution] distribution with shape `alpha`, scale `s`, and location `m` at a probability `p`.

```c
double out = stdlib_base_dists_frechet_quantile( 0.5, 2.0, 3.0, 2.0 );
// returns ~5.603
```

The function accepts the following arguments:

-   **p**: `[in] double` input probability.
-   **alpha**: `[in] double` shape parameter.
-   **s**: `[in] double` scale parameter.
-   **m**: `[in] double` location parameter.

```c
double stdlib_base_dists_frechet_quantile( const double p, const double alpha, const double s, const double m );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/stats/base/dists/frechet/quantile.h"
#include "stdlib/constants/float64/eps.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 alpha;
    double p;
    double s;
    double m;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        p = random_uniform( 0.0, 1.0 );
        alpha = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 5.0 );
        s = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 5.0 );
        m = random_uniform( -2.0, 2.0 );
        y = stdlib_base_dists_frechet_quantile( p, alpha, s, m );
        printf( "p: %lf, α: %lf, s: %lf, m: %lf, Q(p;α,s,m): %lf\n", p, alpha, s, m, 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].

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---

## License

See [LICENSE][stdlib-license].


## Copyright

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

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[frechet-distribution]: https://en.wikipedia.org/wiki/Fr%C3%A9chet_distribution

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

</section>

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