项目作者: stdlib-js

项目描述 :
F distribution differential entropy.
高级语言: Makefile
项目地址: git://github.com/stdlib-js/stats-base-dists-f-entropy.git
创建时间: 2021-06-15T17:10:09Z
项目社区:https://github.com/stdlib-js/stats-base-dists-f-entropy

开源协议:Apache License 2.0

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Entropy

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

[F][f-distribution] distribution [differential entropy][entropy].



The [differential entropy][entropy] (in [nats][nats]) for a [F][f-distribution] random variable is



math h\left( X \right) = \ln\left( \tfrac{d_2}{d_1} \Gamma\left( \tfrac{d_1}{2} \right) \Gamma\left( \tfrac{d_2}{2} \right) \Gamma\left( \tfrac{d_1+d_2}{2} \right) \right) \\ + \left( 1-\tfrac{d_1}{2} \right) \Psi\left( \tfrac{d_1}{2} \right) + \left( 1-\tfrac{d_2}{2} \right) \Psi\left( \tfrac{d_2}{2} \right) + \tfrac{d_1+d_2}{2} \Psi\left( \tfrac{d_1+d_2}{2} \right)





where d1 is the numerator degrees of freedom, d2 is the denominator degrees of freedom, and Γ and Ψ denote the [gamma][gamma-function] and [digamma][digamma] functions, respectively.



## Installation

bash npm install @stdlib/stats-base-dists-f-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-f-entropy' );

#### entropy( d1, d2 )

Returns the [differential entropy][entropy] of an [F][f-distribution] distribution with numerator degrees of freedom d1 and denominator degrees of freedom d2 (in [nats][nats]).

javascript var v = entropy( 4.0, 7.0 ); // returns ~1.277 v = entropy( 4.0, 12.0 ); // returns ~1.12 v = entropy( 8.0, 2.0 ); // returns ~2.144

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

javascript var v = entropy( NaN, 7.0 ); // returns NaN v = entropy( 3.0, NaN ); // returns NaN

If provided d1 <= 0, the function returns NaN.

javascript var v = entropy( 0.0, 2.0 ); // returns NaN v = entropy( -1.0, 1.0 ); // returns NaN

If provided d2 <= 0, the function returns NaN.

javascript var v = entropy( 3.0, 0.0 ); // returns NaN v = entropy( 3.0, -1.0 ); // returns NaN





## Examples



javascript var randu = require( '@stdlib/random-base-randu' ); var EPS = require( '@stdlib/constants-float64-eps' ); var entropy = require( '@stdlib/stats-base-dists-f-entropy' ); var d1; var d2; var v; var i; for ( i = 0; i < 10; i++ ) { d1 = ( randu()*10.0 ) + EPS; d2 = ( randu()*10.0 ) + EPS; v = entropy( d1, d2 ); console.log( 'd1: %d, d2: %d, h(X;d1,d2): %d', d1.toFixed( 4 ), d2.toFixed( 4 ), v.toFixed( 4 ) ); }




## C APIs







### Usage

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

#### stdlib_base_dists_f_entropy( d1, d2 )

Evaluates the [differential entropy][entropy] of an [F][f-distribution] distribution with numerator degrees of freedom d1 and denominator degrees of freedom d2 (in [nats][nats]).

c double out = stdlib_base_dists_f_entropy( 3.0, 7.0 ); // returns ~1.298

The function accepts the following arguments:

- d1: [in] double numerator degrees of freedom.
- d2: [in] double denominator degrees of freedom.

c double stdlib_base_dists_f_entropy( const double d1, const double d2 );





### Examples

c #include "stdlib/stats/base/dists/f/entropy.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 d1; double d2; double y; int i; for ( i = 0; i < 25; i++ ) { d1 = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 ); d2 = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 ); y = stdlib_base_dists_f_entropy( d1, d2 ); printf( "d1: %lf, d2: %lf, h(X;d1,d2): %lf\n", d1, d2, 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].

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## License

See [LICENSE][stdlib-license].


## Copyright

Copyright © 2016-2025. The Stdlib [Authors][stdlib-authors].