npm package: @stdlib/stats-base-dists-exponential-pdf
Description: Exponential distribution probability density function (PDF).
Author: The Stdlib Authors
Latest version: 0.3.1

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# Probability Density Function

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> [Exponential][exponential-distribution] distribution probability density function (PDF).

<section class="intro">

The [probability density function][pdf] (PDF) for an [exponential][exponential-distribution] random variable is

<!-- <equation class="equation" label="eq:exponential_pdf" align="center" raw="f(x;\lambda) = \begin{cases} \lambda e^{-\lambda x} & x \ge 0 \\ 0 & x < 0 \end{cases}" alt="Probability density function (PDF) for a Exponential distribution."> -->

<div class="equation" align="center" data-raw-text="f(x;\lambda) = \begin{cases} \lambda e^{-\lambda x} &amp; x \ge 0 \\ 0 &amp; x &lt; 0 \end{cases}" data-equation="eq:exponential_pdf">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/exponential/pdf/docs/img/equation_exponential_pdf.svg" alt="Probability density function (PDF) for a Exponential distribution.">
    <br>
</div>

<!-- </equation> -->

where `λ` is the rate parameter.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-exponential-pdf
```

</section>

<section class="usage">

## Usage

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

#### pdf( x, lambda )

Evaluates the [probability density function][pdf] (PDF) for an [exponential][exponential-distribution] distribution with rate parameter `lambda`.

```javascript
var y = pdf( 2.0, 0.3 );
// returns ~0.165

y = pdf( 2.0, 1.0 );
// returns ~0.135
```

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

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

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

If provided `lambda < 0`, the function returns `NaN`.

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

#### pdf.factory( lambda )

Partially applies `lambda` to create a reusable `function` for evaluating the [PDF][pdf].

```javascript
var mypdf = pdf.factory( 0.1 );

var y = mypdf( 8.0 );
// returns ~0.045

y = mypdf( 5.0 );
// returns ~0.06
```

</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 pdf = require( '@stdlib/stats-base-dists-exponential-pdf' );

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

logEachMap( 'x: %0.4f, λ: %0.4f, f(x;λ): %0.4f', x, lambda, pdf );
```

</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/exponential/pdf.h"
```

#### stdlib_base_dists_exponential_pdf( x, lambda )

Evaluates the [probability density function][pdf] (PDF) for an [exponential][exponential-distribution] distribution with rate parameter `lambda`.

```c
double out = stdlib_base_dists_exponential_pdf( 2.0, 0.7 );
// returns ~0.173
```

The function accepts the following arguments:

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

```c
double stdlib_base_dists_exponential_pdf( 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/exponential/pdf.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 lambda;
    double x;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x = random_uniform( 0.0, 100.0 );
        lambda = random_uniform( 0.0, 100.0 ) + STDLIB_CONSTANT_FLOAT64_EPS;
        y = stdlib_base_dists_exponential_pdf( x, lambda );
        printf( "x: %lf, λ: %lf, f(x;λ): %lf\n", x, lambda, y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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<section class="references">

</section>

<!-- /.references -->

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<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].

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

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

</section>

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-exponential-pdf/main/LICENSE

[pdf]: https://en.wikipedia.org/wiki/Probability_density_function

[exponential-distribution]: https://en.wikipedia.org/wiki/Exponential_distribution

</section>

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