Entropy

Chi-squared distribution differential entropy.

The differential entropy (in nats) for a chi-squared random variable is

h left-parenthesis upper X right-parenthesis equals StartFraction k Over 2 EndFraction plus ln left-parenthesis 2 normal upper Gamma left-parenthesis StartFraction k Over 2 EndFraction right-parenthesis right-parenthesis plus left-parenthesis 1 minus StartFraction k Over 2 EndFraction right-parenthesis psi left-parenthesis StartFraction k Over 2 EndFraction right-parenthesis

where k > 0 is the degrees of freedom.

Usage

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

entropy( k )

Returns the differential entropy of a chi-squared distribution with degrees of freedom k (in nats).

var v = entropy( 9.0 );
// returns ~2.786

v = entropy( 0.5 );
// returns ~-0.939

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

var v = 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/chisquare/entropy' );

var k;
var v;
var i;

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