Entropy

Beta distribution differential entropy.

The differential entropy for a beta random variable is

where α > 0 is the first shape parameter and β > 0 is the second shape parameter.

Installation

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

Usage

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

entropy( alpha, beta )

Returns the differential entropy of a beta distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

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

v = entropy( 4.0, 12.0 );
// returns ~-0.869

v = entropy( 8.0, 2.0 );
// returns ~-0.795

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 alpha <= 0, the function returns NaN.

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

v = entropy( -1.0, 1.0 );
// returns NaN

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

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

v = entropy( 1.0, -1.0 );
// returns NaN

Examples

var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var EPS = require( '@stdlib/constants-float64-eps' );
var entropy = require( '@stdlib/stats-base-dists-beta-entropy' );

var opts = {
    'dtype': 'float64'
};
var alpha = uniform( 10, EPS, 10.0, opts );
var beta = uniform( 10, EPS, 10.0, opts );

logEachMap( 'α: %0.4f, β: %0.4f, h(X;α,β): %0.4f', alpha, beta, entropy );

C APIs

Usage

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

stdlib_base_dists_beta_entropy( alpha, beta )

Returns the differential entropy of a beta distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

double y = stdlib_base_dists_beta_entropy( 1.0, 1.0 );
// returns 0.0

The function accepts the following arguments:

• alpha: [in] double first shape parameter.
• beta: [in] double second shape parameter.

double stdlib_base_dists_beta_entropy( const double alpha, const double beta );

Examples

#include "stdlib/stats/base/dists/beta/entropy.h"
#include "stdlib/constants/float64/eps.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 alpha;
    double beta;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        alpha = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 );
        beta = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 );
        y = stdlib_base_dists_beta_entropy( alpha, beta );
        printf( "α: %lf, β: %lf, h(X;α,β): %lf\n", alpha, beta, 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.