Entropy

Cauchy distribution differential entropy.

The differential entropy for a Cauchy random variable with location parameter x0 and scale parameter Ɣ > 0 is

Installation

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

Usage

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

entropy( x0, gamma )

Returns the differential entropy of a Cauchy distribution with location parameter x0 and scale parameter gamma (in nats).

var v = entropy( 10.0, 5.0 );
// returns ~4.14

v = entropy( 7.0, 2.0 );
// returns ~3.224

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

var v = entropy( NaN, 5.0 );
// returns NaN

v = entropy( 20.0, NaN );
// returns NaN

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

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

v = entropy( 1.0, 0.0 );
// 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-cauchy-entropy' );

var opts = {
    'dtype': 'float64'
};
var gamma = uniform( 10, EPS, 10.0, opts );
var x0 = uniform( 10, 0.0, 100.0, opts );

logEachMap( 'x0: %0.4f, γ: %0.4f, h(X;x0,γ): %0.4f', x0, gamma, entropy );

C APIs

Usage

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

stdlib_base_dists_cauchy_entropy( x0, gamma )

Evaluates the differential entropy of a Cauchy distribution with location parameter x0 and scale parameter gamma (in nats).

double out = stdlib_base_dists_cauchy_entropy( 10.0, 5.0 );
// returns ~4.14

The function accepts the following arguments:

• x0: [in] double location parameter.
• gamma: [in] double scale parameter.

double stdlib_base_dists_cauchy_entropy( const double x0, const double gamma );

Examples

#include "stdlib/stats/base/dists/cauchy/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 gamma;
    double x0;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x0 = random_uniform( 0.0, 100.0 );
        gamma = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 );
        y = stdlib_base_dists_cauchy_entropy( x0, gamma );
        printf( "x0: %lf, γ: %lf, h(X;x0,γ): %lf\n", x0, gamma, 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.