Entropy

Rayleigh distribution differential entropy.

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

h left-parenthesis upper X right-parenthesis equals 1 plus ln left-parenthesis StartFraction sigma Over StartRoot 2 EndRoot EndFraction right-parenthesis plus StartFraction gamma Over 2 EndFraction

where σ > 0 is the scale parameter.

Usage

var entropy = require( '@stdlib/math/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/math/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 ) );
}