Entropy

Bernoulli distribution entropy.

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

where p is the success probability and q = 1 - p.

Usage

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

entropy( p )

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

var v = entropy( 0.1 );
// returns ~0.325

v = entropy( 0.5 );
// returns ~0.693

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/stats/base/dists/bernoulli/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 ) );
}

C APIs

Usage

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

stdlib_base_dists_bernoulli_entropy( p )

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

double out = stdlib_base_dists_bernoulli_entropy( 0.1 );
// returns ~0.325

The function accepts the following arguments:

p: [in] double success probability.

double stdlib_base_dists_bernoulli_entropy( const double p );

Examples

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

int main( void ) {
    double p;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        p = (double)rand() / ( (double)RAND_MAX + 1.0 );
        y = stdlib_base_dists_bernoulli_entropy( p );
        printf( "x: %lf, H(X;p): %lf\n", p, y );
    }
}