Entropy

Beta distribution differential entropy.

The differential entropy for a beta random variable is

h left-parenthesis upper X right-parenthesis equals ln left-parenthesis upper B e t a left-parenthesis alpha comma beta right-parenthesis right-parenthesis minus left-parenthesis alpha minus 1 right-parenthesis psi left-parenthesis alpha right-parenthesis minus left-parenthesis beta minus 1 right-parenthesis psi left-parenthesis beta right-parenthesis plus left-parenthesis alpha plus beta minus 2 right-parenthesis psi left-parenthesis alpha plus beta right-parenthesis

where α > 0 is the first shape parameter and β > 0 is the second shape parameter.

Usage

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

entropy( alpha, beta )

Returns the differential entropy of a beta distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var v = entropy( 1.0, 1.0 );
// returns 0.0

v = entropy( 4.0, 12.0 );
// returns ~-0.869

v = entropy( 8.0, 2.0 );
// returns ~-0.795

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

var v = entropy( NaN, 2.0 );
// returns NaN

v = entropy( 2.0, NaN );
// returns NaN

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

var v = entropy( 0.0, 1.0 );
// returns NaN

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

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

var v = entropy( 1.0, 0.0 );
// returns NaN

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

Examples

var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/math/float64-eps' );
var entropy = require( '@stdlib/math/base/dists/beta/entropy' );

var alpha;
var beta;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    alpha = ( randu()*10.0 ) + EPS;
    beta = ( randu()*10.0 ) + EPS;
    v = entropy( alpha, beta );
    console.log( 'α: %d, β: %d, h(X;α,β): %d', alpha.toFixed( 4 ), beta.toFixed( 4 ), v.toFixed( 4 ) );
}