npm package: @stdlib/stats-base-dists-planck-quantile
Description: Planck (discrete exponential) distribution quantile function.
Author: The Stdlib Authors
Latest version: 0.1.1

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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] -->

> Planck (discrete exponential) distribution [quantile function][quantile-function].

<section class="intro">

The [quantile function][quantile-function] for a Planck random variable is

<!-- <equation class="equation" label="eq:planck_quantile_function" align="center" raw="Q(p;\lambda) = \left\lceil -\frac{\ln(1-p)}{\lambda} - 1 \right\rceil" alt="Quantile function for a Planck distribution."> -->

<!-- </equation> -->

for `0 < p < 1` and where `λ` is the shape parameter.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### quantile( p, lambda )

Evaluates the [quantile function][quantile-function] for a Planck distribution with shape parameter `lambda` at a probability `p`.

```javascript
var y = quantile( 0.8, 0.4 );
// returns 4.0

y = quantile( 0.5, 1.4 );
// returns 0.0

y = quantile( 0.9, 2.1 );
// returns 1.0
```

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

```javascript
var y = quantile( 1.9, 0.5 );
// returns NaN

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

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 shape parameter `lambda` which is nonpositive, the function returns `NaN`.

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

#### quantile.factory( lambda )

Returns a function for evaluating the [quantile function][quantile-function] for a Planck distribution with shape parameter `lambda`.

```javascript
var myquantile = quantile.factory( 0.4 );
var y = myquantile( 0.4 );
// returns 1.0

y = myquantile( 0.8 );
// returns 4.0

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

</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-planck-quantile' );

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

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

</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/planck/quantile.h"
```

#### stdlib_base_dists_planck_quantile( p, lambda )

Evaluates the [quantile function][quantile-function] for a Planck (discrete exponential) distribution with probability `p` and shape parameter `lambda`.

```c
double out = stdlib_base_dists_planck_quantile( 0.8, 0.4 );
// returns 4.0
```

The function accepts the following arguments:

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

```c
double stdlib_base_dists_planck_quantile( const double p, const double lambda );
```

</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/planck/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 lambda;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        p = random_uniform( 0.0, 1.0 );
        lambda = random_uniform( 0.1, 5.0 );
        y = stdlib_base_dists_planck_quantile( p, lambda );
        printf( "p: %lf, λ: %lf, Q(p;λ): %lf\n", p, lambda, 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].

</section>

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

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