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]

> [Gumbel][gumbel-distribution] distribution [differential entropy][entropy].

The [differential entropy][entropy] for a [gumbel][gumbel-distribution] random variable with location μ and scale β is

Differential entropy for a gumbel distribution.

where γ is the [Euler–Mascheroni constant][euler-mascheroni].

Installation

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

`Usage`

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

#### entropy( mu, beta )

Returns the [differential entropy][entropy] for a [Gumbel][gumbel-distribution] distribution with location parameter mu and scale parameter beta (in [nats][nats]).

`javascript var y = entropy( 2.0, 1.0 ); // returns ~1.577

y = entropy( 0.0, 1.0 ); // returns ~1.577

y = entropy( -1.0, 4.0 ); // returns ~2.964`

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

`javascript var y = entropy( NaN, 1.0 ); // returns NaN

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

If provided beta <= 0, the function returns NaN.

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

y = entropy( 0.0, -1.0 ); // returns NaN`

`Examples`

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

var opts = { 'dtype': 'float64' }; var beta = uniform( 10, 0.0, 20.0, opts ); var mu = uniform( 10, -5.0, 5.0, opts );

logEachMap( 'µ: %0.4f, β: %0.4f, h(X;µ,β): %0.4f', mu, beta, entropy );`

*

`C APIs`

`$3`

`c #include "stdlib/stats/base/dists/gumbel/entropy.h"`

#### stdlib_base_dists_gumbel_entropy( mu, beta )

Returns the [differential entropy][entropy] for a [Gumbel][gumbel-distribution] distribution with location parameter mu and scale parameter beta (in [nats][nats]).

`c double out = stdlib_base_dists_gumbel_entropy( 0.0, 1.0 ); // returns ~1.577`

The function accepts the following arguments:

- mu: [in] doublelocation parameter. - beta:[in] double scale parameter.

`c double stdlib_base_dists_gumbel_entropy( const double mu, const double beta );`

`$3`

`c #include "stdlib/stats/base/dists/gumbel/entropy.h" #include #include

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 beta; double mu; double y; int i;

for ( i = 0; i < 25; i++ ) { mu = random_uniform( 0.0, 10.0 ); beta = random_uniform( 0.0, 10.0 ); y = stdlib_base_dists_gumbel_entropy( mu, beta ); printf( "µ: %lf, β: %lf, h(X;µ,β): %lf\n", mu, beta, y ); } }`

*

`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`

[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-gumbel-entropy.svg [npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-gumbel-entropy

[test-image]: https://github.com/stdlib-js/stats-base-dists-gumbel-entropy/actions/workflows/test.yml/badge.svg?branch=v0.3.1 [test-url]: https://github.com/stdlib-js/stats-base-dists-gumbel-entropy/actions/workflows/test.yml?query=branch:v0.3.1

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-gumbel-entropy/main.svg [coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-gumbel-entropy?branch=main

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com

[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-gumbel-entropy/tree/deno [deno-readme]: https://github.com/stdlib-js/stats-base-dists-gumbel-entropy/blob/deno/README.md [umd-url]: https://github.com/stdlib-js/stats-base-dists-gumbel-entropy/tree/umd [umd-readme]: https://github.com/stdlib-js/stats-base-dists-gumbel-entropy/blob/umd/README.md [esm-url]: https://github.com/stdlib-js/stats-base-dists-gumbel-entropy/tree/esm [esm-readme]: https://github.com/stdlib-js/stats-base-dists-gumbel-entropy/blob/esm/README.md [branches-url]: https://github.com/stdlib-js/stats-base-dists-gumbel-entropy/blob/main/branches.md

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

[euler-mascheroni]: https://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant

[gumbel-distribution]: https://en.wikipedia.org/wiki/Gumbel_distribution

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

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


  
    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]

> [Gumbel][gumbel-distribution] distribution [differential entropy][entropy].

The [differential entropy][entropy] for a [gumbel][gumbel-distribution] random variable with location μ and scale β is

where γ is the [Euler–Mascheroni constant][euler-mascheroni].

`Installation`

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

`Usage`

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

#### entropy( mu, beta )

Returns the [differential entropy][entropy] for a [Gumbel][gumbel-distribution] distribution with location parameter mu and scale parameter beta (in [nats][nats]).

`javascript var y = entropy( 2.0, 1.0 ); // returns ~1.577

y = entropy( 0.0, 1.0 ); // returns ~1.577

y = entropy( -1.0, 4.0 ); // returns ~2.964 `

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

`javascript var y = entropy( NaN, 1.0 ); // returns NaN

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

If provided beta <= 0, the function returns NaN.

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

y = entropy( 0.0, -1.0 ); // returns NaN `

`Examples`

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

var opts = { 'dtype': 'float64' }; var beta = uniform( 10, 0.0, 20.0, opts ); var mu = uniform( 10, -5.0, 5.0, opts );

logEachMap( 'µ: %0.4f, β: %0.4f, h(X;µ,β): %0.4f', mu, beta, entropy ); `

*

`C APIs`

`$3`

`c #include "stdlib/stats/base/dists/gumbel/entropy.h" `

#### stdlib_base_dists_gumbel_entropy( mu, beta )

Returns the [differential entropy][entropy] for a [Gumbel][gumbel-distribution] distribution with location parameter mu and scale parameter beta (in [nats][nats]).

`c double out = stdlib_base_dists_gumbel_entropy( 0.0, 1.0 ); // returns ~1.577 `

The function accepts the following arguments:

- mu: [in] double location parameter. - beta: [in] double scale parameter.

`c double stdlib_base_dists_gumbel_entropy( const double mu, const double beta ); `

`$3`

`c #include "stdlib/stats/base/dists/gumbel/entropy.h" #include #include

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 beta; double mu; double y; int i;

for ( i = 0; i < 25; i++ ) { mu = random_uniform( 0.0, 10.0 ); beta = random_uniform( 0.0, 10.0 ); y = stdlib_base_dists_gumbel_entropy( mu, beta ); printf( "µ: %lf, β: %lf, h(X;µ,β): %lf\n", mu, beta, y ); } } `

*

`Notice`

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`

[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-gumbel-entropy.svg [npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-gumbel-entropy

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com

[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

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

[euler-mascheroni]: https://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant

[gumbel-distribution]: https://en.wikipedia.org/wiki/Gumbel_distribution

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

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