Entropy

F distribution differential entropy.

The differential entropy (in nats) for a F random variable is

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

Installation

npm install @stdlib/stats-base-dists-f-entropy

Usage

var entropy = require( '@stdlib/stats-base-dists-f-entropy' );

entropy( d1, d2 )

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

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.

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

v = entropy( 3.0, NaN );
// returns NaN

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

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.

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

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

Examples

var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var EPS = require( '@stdlib/constants-float64-eps' );
var entropy = require( '@stdlib/stats-base-dists-f-entropy' );

var opts = {
    'dtype': 'float64'
};
var d1 = uniform( 10, EPS, 10.0, opts );
var d2 = uniform( 10, EPS, 20.0, opts );

logEachMap( 'd1: %0.4f, d2: %0.4f, h(X;d1,d2): %0.4f', d1, d2, entropy );

C APIs

Usage

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

stdlib_base_dists_f_entropy( d1, d2 )

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

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.

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

Examples

#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, 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, see the main project repository.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.