Entropy

Normal distribution differential entropy.

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

Installation

npm install @stdlib/stats-base-dists-normal-entropy

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 uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var entropy = require( '@stdlib/stats-base-dists-normal-entropy' );

var opts = {
    'dtype': 'float64'
};
var sigma = uniform( 10, 0.0, 20.0, opts );
var mu = uniform( 10, -5.0, 5.0, opts );

logEachMap( 'µ: %0.4f, σ: %0.4f, h(X;µ,σ): %0.4f', mu, sigma, entropy );

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 );
    }
}

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.