Entropy

Chi-squared distribution differential entropy.

The differential entropy (in nats) for a chi-squared random variable is

where k > 0 is the degrees of freedom.

Usage

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

entropy( k )

Returns the differential entropy of a chi-squared distribution with degrees of freedom k (in nats).

var v = entropy( 9.0 );
// returns ~2.786

v = entropy( 0.5 );
// returns ~-0.939

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

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

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var entropy = require( '@stdlib/stats/base/dists/chisquare/entropy' );

var k;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    k = randu() * 20.0;
    v = entropy( k );
    console.log( 'k: %d, entropy(X,k): %d', k.toFixed( 4 ), v.toFixed( 4 ) );
}

C APIs

Usage

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

stdlib_base_dists_chisquare_entropy( k )

Evaluates the differential entropy of a chi-squared distribution with degrees of freedom k (in nats).

double out = stdlib_base_dists_chisquare_entropy( 9.0 );
// returns ~2.786

The function accepts the following arguments:

k: [in] double degrees of freedom.

double stdlib_base_dists_chisquare_entropy( const double k );

Examples

#include "stdlib/stats/base/dists/chisquare/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 k;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        k = random_uniform( 0.0, 20.0 );
        y = stdlib_base_dists_chisquare_entropy( k );
        printf( "k: %lf, entropy(X,k): %lf\n", k, y );
    }
}