Entropy

Geometric distribution entropy.

The entropy (in nats) for a geometric random variable is

upper H left-parenthesis upper X right-parenthesis equals StartFraction minus left-parenthesis 1 minus p right-parenthesis ln left-parenthesis 1 minus p right-parenthesis minus p ln left-parenthesis p right-parenthesis Over p EndFraction

where p is the success probability.

Usage

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

entropy( p )

Returns the entropy of a geometric distribution with success probability p (in nats).

var v = entropy( 0.1 );
// returns ~3.251

v = entropy( 0.5 );
// returns ~1.386

If provided a success probability p outside of [0,1], the function returns NaN.

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

v = entropy( 1.5 );
// returns NaN

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/geometric/entropy' );

var v;
var i;
var p;

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