Entropy

Normal distribution differential entropy.

The differential entropy (in nats) for a normal random variable with mean μ and standard deviation σ > 0 is

Usage

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

entropy( mu, sigma )

Returns the differential entropy for a normal distribution with mean mu and standard deviation sigma (in nats).

var y = entropy( 2.0, 1.0 );
// returns ~1.419

y = entropy( -1.0, 4.0 );
// returns ~2.805

If provided NaN as any argument, the function returns NaN.

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

y = entropy( 0.0, NaN );
// returns NaN

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

var y = entropy( 0.0, 0.0 );
// returns NaN

y = entropy( 0.0, -1.0 );
// returns NaN

Examples

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

var sigma;
var mu;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    mu = ( randu()*10.0 ) - 5.0;
    sigma = randu() * 20.0;
    y = entropy( mu, sigma );
    console.log( 'µ: %d, σ: %d, h(X;µ,σ): %d', mu.toFixed( 4 ), sigma.toFixed( 4 ), y.toFixed( 4 ) );
}

C APIs

Usage

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

stdlib_base_dists_normal_entropy( mu, sigma )

Evaluates the differential entropy of a normal distribution.

double out = stdlib_base_dists_normal_entropy( 0.0, 1.0 );
// returns ~1.4189

The function accepts the following arguments:

mu: [in] double mean.
sigma: [in] double standard deviation.

double stdlib_base_dists_normal_entropy( const double mu, const double sigma );

Examples

#include "stdlib/stats/base/dists/normal/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 mu;
    double sigma;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        mu = random_uniform( -5.0, 5.0 );
        sigma = random_uniform( 0.1, 20.0 );
        y = stdlib_base_dists_normal_entropy( mu, sigma );
        printf( "\u00b5: %.4f, \u03c3: %.4f, h(X;\u00b5,\u03c3): %.4f\n", mu, sigma, y );
    }
}