Entropy

Lévy distribution differential entropy.

The differential entropy (in nats) for a Lévy random variable with location μ and scale c > 0 is

h left-parenthesis upper X right-parenthesis equals StartFraction 1 plus 3 gamma plus ln left-parenthesis 16 pi c squared right-parenthesis Over 2 EndFraction

where γ is the Euler-Mascheroni constants.

Usage

var entropy = require( '@stdlib/math/base/dists/levy/entropy' );

entropy( mu, c )

Returns the differential entropy for a Lévy distribution with location parameter mu and scale parameter c (in nats).

var y = entropy( 2.0, 1.0 );
// returns ~3.324

y = entropy( 0.0, 1.0 );
// returns ~3.324

y = entropy( -1.0, 4.0 );
// returns ~4.711

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

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

y = entropy( 0.0, NaN );
// returns NaN

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

var y = entropy( 0.0, 0.0 );
// returns NaN

y = entropy( 0.0, -1.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var entropy = require( '@stdlib/math/base/dists/levy/entropy' );

var mu;
var c;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    mu = ( randu()*10.0 ) - 5.0;
    c = randu() * 20.0;
    y = entropy( mu, c );
    console.log( 'µ: %d, c: %d, h(X;µ,c): %d', mu.toFixed( 4 ), c.toFixed( 4 ), y.toFixed( 4 ) );
}