Entropy

Student's t distribution differential entropy.

The differential entropy (in nats) for a Student's t random variable with degrees of freedom ν is

h left-parenthesis upper X right-parenthesis equals StartFraction nu plus 1 Over 2 EndFraction left-bracket psi left-parenthesis StartFraction 1 plus nu Over 2 EndFraction right-parenthesis minus psi left-parenthesis StartFraction nu Over 2 EndFraction right-parenthesis right-bracket plus ln left-bracket StartRoot nu EndRoot upper B left-parenthesis StartFraction nu Over 2 EndFraction comma one-half right-parenthesis right-bracket

where Β and ψ denote the beta and digamma functions, respectively.

Usage

var entropy = require( '@stdlib/math/base/dists/t/entropy' );

entropy( v )

Returns the differential entropy of a Student's t distribution with degrees of freedom v (in nats).

var y = entropy( 9.0 );
// returns ~1.533

y = entropy( 3.5 );
// returns ~1.721

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

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

y = entropy( 0.0 );
// 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/t/entropy' );

var v;
var y;
var i;

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