F distribution differential entropy.
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!
[![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].
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)
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.bash
npm install @stdlib/stats-base-dists-f-entropy
script
tag without installation and bundlers, use the [ES Module][es-module] available on the [esm
][esm-url] branch (see [README][esm-readme]).deno
][deno-url] branch (see [README][deno-readme] for usage intructions).umd
][umd-url] branch (see [README][umd-readme]).javascript
var entropy = require( '@stdlib/stats-base-dists-f-entropy' );
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
NaN
as any argument, the function returns NaN
.javascript
var v = entropy( NaN, 7.0 );
// returns NaN
v = entropy( 3.0, NaN );
// returns NaN
d1 <= 0
, the function returns NaN
.javascript
var v = entropy( 0.0, 2.0 );
// returns NaN
v = entropy( -1.0, 1.0 );
// returns NaN
d2 <= 0
, the function returns NaN
.javascript
var v = entropy( 3.0, 0.0 );
// returns NaN
v = entropy( 3.0, -1.0 );
// returns NaN
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
#include "stdlib/stats/base/dists/f/entropy.h"
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
[in] double
numerator degrees of freedom.[in] double
denominator degrees of freedom.c
double stdlib_base_dists_f_entropy( const double d1, const double d2 );
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 );
}
}