npm package: @stdlib/stats-base-dists-poisson-entropy
Description: Poisson distribution entropy.
Author: The Stdlib Authors
Latest version: 0.2.3

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# Entropy

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

> [Poisson][poisson-distribution] distribution [entropy][entropy].

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<section class="intro">

The [entropy][entropy] (in [nats][nats]) for a [Poisson][poisson-distribution] random variable is

<!-- <equation class="equation" label="eq:poisson_entropy" align="center" raw="H\left( X \right) = \lambda [1-\log(\lambda )]+e^{-\lambda }\sum_{k=0}^{\infty }{\frac{\lambda ^{k}\log(k!)}{k!}}" alt="Entropy for a Poisson distribution."> -->

<div class="equation" align="center" data-raw-text="H\left( X \right) = \lambda [1-\log(\lambda )]+e^{-\lambda }\sum_{k=0}^{\infty }{\frac{\lambda ^{k}\log(k!)}{k!}}" data-equation="eq:poisson_entropy">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/poisson/entropy/docs/img/equation_poisson_entropy.svg" alt="Entropy for a Poisson distribution.">
    <br>
</div>

<!-- </equation> -->

where `λ` is the mean parameter.

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-poisson-entropy
```

</section>

<section class="usage">

## Usage

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

#### entropy( lambda )

Returns the [entropy][entropy] of a [Poisson][poisson-distribution] distribution with mean parameter `lambda` (in [nats][nats]).

```javascript
var v = entropy( 9.0 );
// returns ~2.508

v = entropy( 0.5 );
// returns ~0.928
```

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

```javascript
var v = entropy( -1.0 );
// returns NaN
```

</section>

<!-- /.usage -->

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<section class="notes">

</section>

<!-- /.notes -->

<!-- Package usage examples. -->

<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 entropy = require( '@stdlib/stats-base-dists-poisson-entropy' );

var opts = {
    'dtype': 'float64'
};
var lambda = uniform( 10, 0.0, 20.0, opts );

logEachMap( 'λ: %0.4f, H(X;λ): %0.4f', lambda, entropy );
```

</section>

<!-- /.examples -->

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* * *

## 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].

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

[poisson-distribution]: https://en.wikipedia.org/wiki/Poisson_distribution

[entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29

[nats]: https://en.wikipedia.org/wiki/Nat_%28unit%29

</section>

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