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

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# Probability Mass 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 [probability mass function][pmf] (PMF).

<section class="intro">

The [probability mass function][pmf] (PMF) for a Planck random variable is defined as

<!-- <equation class="equation" label="eq:planck_pmf" align="center" raw="\Pr(X = x, \lambda) = \begin{cases}(1 - e^{-\lambda})e^{-\lambda x} & \text{for } x = 0, 1, 2, \ldots \\ 0 & \text{otherwise} \end{cases}" alt="Probability mass function (PMF) for a Planck (discrete exponential) distribution."> -->

<!-- </equation> -->

where `λ` is the shape parameter. The random variable `X` denotes the count of events in a quantized system.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### pmf( x, lambda )

Evaluates the [probability mass function][pmf] (PMF) of a Planck (discrete exponential) distribution with shape parameter `lambda`.

```javascript
var y = pmf( 4.0, 0.3 );
// returns ~0.0781

y = pmf( 2.0, 1.7 );
// returns ~0.0273

y = pmf( -1.0, 2.5 );
// returns 0.0
```

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

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

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

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

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

#### pmf.factory( lambda )

Returns a function for evaluating the [probability mass function][pmf] (PMF) of a Planck (discrete exponential) distribution with shape parameter `lambda`.

```javascript
var mypmf = pmf.factory( 0.5 );
var y = mypmf( 3.0 );
// returns ~0.0878

y = mypmf( 1.0 );
// returns ~0.2387
```

</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 pmf = require( '@stdlib/stats-base-dists-planck-pmf' );

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

logEachMap( 'x: %d, λ: %0.4f, P(X = x; λ): %0.4f', x, lambda, pmf );
```

</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/pmf.h"
```

#### stdlib_base_dists_planck_pmf( x, lambda )

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

```c
double out = stdlib_base_dists_planck_pmf( 4.0, 0.3 );
// returns ~0.0781
```

The function accepts the following arguments:

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

```c
double stdlib_base_dists_planck_pmf( 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/pmf.h"
#include "stdlib/math/base/special/round.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 x;
    double lambda;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x = stdlib_base_round( random_uniform( 0.0, 11.0 ) );
        lambda = random_uniform( 0.1, 5.0 );
        y = stdlib_base_dists_planck_pmf( x, lambda );
        printf( "x: %.0f, λ: %lf, P(X = x; λ): %lf\n", x, 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].

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[pmf]: https://en.wikipedia.org/wiki/Probability_mass_function

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