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

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# Cumulative Distribution 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 [cumulative distribution function][cdf].

<section class="intro">

The [cumulative distribution function][cdf] for a Planck random variable is

<!-- <equation class="equation" label="eq:planck_cdf" align="center" raw="F(x;\lambda) = 1 - e^{-\lambda \cdot (\lfloor x \rfloor + 1)}" alt="CDF for a Planck distribution."> -->

<!-- </equation> -->

where `λ` is the shape parameter and `x` denotes the count of events in a quantized system.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### cdf( x, lambda )

Evaluates the [cumulative distribution function][cdf] for a Planck (discrete exponential) distribution with shape parameter `lambda`.

```javascript
var y = cdf( 2.0, 0.5 );
// returns ~0.7769

y = cdf( 2.0, 1.5 );
// returns ~0.9889
```

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

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

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

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

```javascript
var y = cdf( 2.0, -1.0 );
// returns NaN
```

#### cdf.factory( lambda )

Returns a function for evaluating the [cumulative distribution function][cdf] of a Planck (discrete exponential) distribution with shape parameter `lambda`.

```javascript
var mycdf = cdf.factory( 1.5 );
var y = mycdf( 3.0 );
// returns ~0.9975

y = mycdf( 1.0 );
// returns ~0.9502
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var cdf = require( '@stdlib/stats-base-dists-planck-cdf' );

var opts = {
    'dtype': 'float64'
};
var x = discreteUniform( 10, 0, 5, opts );
var lambda = uniform( 10, 0.1, 5.0, opts );

logEachMap( 'x: %d, λ: %04f, F(x;λ): %04f', x, lambda, cdf );
```

</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/cdf.h"
```

#### stdlib_base_dists_planck_cdf( x, lambda )

Evaluates the [cumulative distribution function][cdf] for a Planck (discrete exponential) distribution with input value `x` and shape parameter `lambda`.

```c
double out = stdlib_base_dists_planck_cdf( 2.0, 0.5 );
// returns ~0.7769
```

The function accepts the following arguments:

-   **x**: `[in] double` input value.
-   **lambda**: `[in] double` shape parameter.

```c
double stdlib_base_dists_planck_cdf( const double x, 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/cdf.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 lambda;
    double x;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x = random_uniform( 0.0, 11.0 );
        lambda = random_uniform( 0.1, 5.0 );
        y = stdlib_base_dists_planck_cdf( x, lambda );
        printf( "x: %lf, λ: %lf, F(x;λ): %lf\n", x, lambda, y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- 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].

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---

## License

See [LICENSE][stdlib-license].


## Copyright

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

</section>

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[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function

</section>

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