Entropy

Cauchy distribution differential entropy.

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

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 randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/float64/eps' );
var entropy = require( '@stdlib/stats/base/dists/cauchy/entropy' );

var gamma;
var x0;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    x0 = randu() * 100.0;
    gamma = ( randu()*10.0 ) + EPS;
    v = entropy( x0, gamma );
    console.log( 'x0: %d, γ: %d, h(X;x0,γ): %d', x0.toFixed( 4 ), gamma.toFixed( 4 ), v.toFixed( 4 ) );
}

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, gamma: %lf, F(x0;gamma): %lf\n", x0, gamma, y );
    }
}