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https://github.com/stdlib-js/stats-base-dists-erlang-entropy
Erlang distribution differential entropy.
https://github.com/stdlib-js/stats-base-dists-erlang-entropy
continuous dist distribution entropy erlang information javascript nats node node-js nodejs prob probability shannon statistics stats stdlib univariate
Last synced: 1 day ago
JSON representation
Erlang distribution differential entropy.
- Host: GitHub
- URL: https://github.com/stdlib-js/stats-base-dists-erlang-entropy
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-15T17:30:12.000Z (over 3 years ago)
- Default Branch: main
- Last Pushed: 2024-09-01T11:45:56.000Z (27 days ago)
- Last Synced: 2024-09-01T23:43:24.634Z (27 days ago)
- Topics: continuous, dist, distribution, entropy, erlang, information, javascript, nats, node, node-js, nodejs, prob, probability, shannon, statistics, stats, stdlib, univariate
- Language: JavaScript
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 1.17 MB
- Stars: 1
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
Awesome Lists containing this project
README
About stdlib...
We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.
The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.
When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.
To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!
# Entropy
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> [Erlang][erlang-distribution] distribution [differential entropy][entropy].
The [differential entropy][entropy] for an [Erlang][erlang-distribution] random variable with shape `k` and rate `λ` is
```math
h\left( X \right) = (1\,-\,k)\psi (k)\,+\,\ln \left[{\frac {\Gamma (k)}{\lambda }}\right]\,+\,k
```
where `Γ` and `Ψ` denote the [gamma][gamma-function] and [digamma][digamma] function, respectively.
## Installation
```bash
npm install @stdlib/stats-base-dists-erlang-entropy
```
Alternatively,
- To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).
The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.
To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
## Usage
```javascript
var entropy = require( '@stdlib/stats-base-dists-erlang-entropy' );
```
#### entropy( k, lambda )
Returns the [differential entropy][entropy] of an [Erlang][erlang-distribution] distribution with parameters shape `k` and rate `lambda` (in [nats][nats]).
```javascript
var v = entropy( 1, 1.0 );
// returns 1.0
v = entropy( 4, 12.0 );
// returns ~-0.462
v = entropy( 8, 2.0 );
// returns ~1.723
```
If provided `NaN` as any argument, the function returns `NaN`.
```javascript
var v = entropy( NaN, 2.0 );
// returns NaN
v = entropy( 2.0, NaN );
// returns NaN
```
If not provided a positive integer for `k`, the function returns `NaN`.
```javascript
var v = entropy( 1.8, 1.0 );
// returns NaN
v = entropy( -1.0, 1.0 );
// returns NaN
```
If provided `lambda <= 0`, the function returns `NaN`.
```javascript
var v = entropy( 2, 0.0 );
// returns NaN
v = entropy( 2, -1.0 );
// returns NaN
```
## Examples
```javascript
var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var EPS = require( '@stdlib/constants-float64-eps' );
var entropy = require( '@stdlib/stats-base-dists-erlang-entropy' );
var lambda;
var k;
var v;
var i;
for ( i = 0; i < 10; i++ ) {
k = round( randu()*10.0 );
lambda = ( randu()*10.0 ) + EPS;
v = entropy( k, lambda );
console.log( 'k: %d, λ: %d, h(X;k,λ): %d', k.toFixed( 4 ), lambda.toFixed( 4 ), v.toFixed( 4 ) );
}
```
* * *
## 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 © 2016-2024. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-erlang-entropy.svg
[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-erlang-entropy
[test-image]: https://github.com/stdlib-js/stats-base-dists-erlang-entropy/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/stats-base-dists-erlang-entropy/actions/workflows/test.yml?query=branch:main
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-erlang-entropy/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-erlang-entropy?branch=main
[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg
[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im
[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/stats-base-dists-erlang-entropy/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-erlang-entropy/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-erlang-entropy/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-erlang-entropy/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-erlang-entropy/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-erlang-entropy/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-erlang-entropy/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-erlang-entropy/main/LICENSE
[erlang-distribution]: https://en.wikipedia.org/wiki/Erlang_distribution
[entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29
[nats]: https://en.wikipedia.org/wiki/Nat_%28unit%29
[gamma-function]: https://en.wikipedia.org/wiki/Gamma_function
[digamma]: https://en.wikipedia.org/wiki/Digamma_function