Entropy

Uniform distribution differential entropy.

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

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

Usage

var entropy = require( '@stdlib/stats/base/dists/uniform/entropy' );

entropy( a, b )

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

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

v = entropy( 4.0, 12.0 );
// returns ~2.079

v = entropy( 2.0, 8.0 );
// returns ~1.792

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 a >= b, the function returns NaN.

var y = entropy( 3.0, 2.0 );
// returns NaN

y = entropy( 3.0, 3.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var entropy = require( '@stdlib/stats/base/dists/uniform/entropy' );

var a;
var b;
var v;
var i;

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

C APIs

Usage

#include "stdlib/stats/base/dists/uniform/entropy.h"

stdlib_base_dists_uniform_entropy( a, b )

Evaluates the entropy of a uniform distribution with minimum support a and maximum support b.

double out = stdlib_base_dists_uniform_entropy( 2.0, 8.0 );
// returns ~1.792

The function accepts the following arguments:

a: [in] double minimum support.
b: [in] double maximum support.

double stdlib_base_dists_uniform_entropy( const double a, const double b );

Examples

#include "stdlib/stats/base/dists/uniform/entropy.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double a;
    double b;
    double v;
    double i;

    for ( i = 0; i < 25; i++ ) {
        a = random_uniform( 0.0, 10.0 );
        b = random_uniform( a, a+10.0 );
        v = stdlib_base_dists_uniform_entropy( a, b );
        printf( "a: %lf, b: %lf, h(X;a,b): %lf\n", a, b, v );
    }
}