Entropy

Rayleigh distribution differential entropy.

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

where σ > 0 is the scale parameter.

Usage

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

entropy( sigma )

Returns the differential entropy of a Rayleigh distribution with scale sigma (in nats).

var y = entropy( 9.0 );
// returns ~3.139

y = entropy( 3.5 );
// returns ~2.195

If provided sigma < 0, the function returns NaN.

var y = entropy( -1.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var entropy = require( '@stdlib/stats/base/dists/rayleigh/entropy' );

var sigma;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    sigma = randu() * 20.0;
    y = entropy( sigma );
    console.log( 'sigma: %d, h(X,v): %d', sigma.toFixed( 4 ), y.toFixed( 4 ) );
}

C APIs

Usage

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

stdlib_base_dists_rayleigh_entropy( sigma )

Returns the differential entropy of a Rayleigh distribution.

double out = stdlib_base_dists_rayleigh_entropy( 9.0 );
// returns ~3.139

The function accepts the following arguments:

sigma: [in] double scale parameter.

double stdlib_base_dists_rayleigh_entropy( const double sigma );

Examples

#include "stdlib/stats/base/dists/rayleigh/entropy.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 sigma;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        sigma = random_uniform( 0.0, 20.0 );
        y = stdlib_base_dists_rayleigh_entropy( sigma );
        printf( "σ: %lf, h(σ): %lf\n", sigma, y );
    }
}