Entropy

Discrete uniform distribution entropy.

The entropy (in nats) for a discrete uniform random variable is

h left-parenthesis upper X right-parenthesis equals ln left-parenthesis b minus a plus 1 right-parenthesis

where a is the minimum support and b is the maximum support. The parameters must satisfy a < b.

Usage

var entropy = require( '@stdlib/math/base/dists/discrete-uniform/entropy' );

entropy( a, b )

Returns the entropy of a discrete uniform distribution with minimum support a and maximum support b (in nats).

var v = entropy( 0, 1 );
// returns ~0.693

v = entropy( 4, 12 );
// returns ~2.197

v = entropy( 2, 8 );
// returns ~1.946

If a or b is not an integer value, the function returns NaN.

var v = entropy( 0.1, 2 );
// returns NaN

v = entropy( 0, 2.2 );
// returns NaN

v = entropy( NaN, 2 );
// returns NaN

v = entropy( 2, NaN );
// returns NaN

If provided a > b, the function returns NaN.

var v = entropy( 3, 2 );
// returns NaN

v = entropy( -1, -2 );
// returns NaN

Examples

var randint = require( '@stdlib/random/base/discrete-uniform' );
var entropy = require( '@stdlib/math/base/dists/discrete-uniform/entropy' );

var randa = randint.factory( 0, 10 );
var randb = randint.factory();
var a;
var b;
var v;
var i;

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