Entropy

Inverse gamma distribution differential entropy.

The differential entropy (in nats) for an inverse gamma random variable is

where α > 0 is the shape parameter, β > 0 is the rate parameter, Γ and denotes the gamma and Ψ the digamma function.

Usage

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

entropy( alpha, beta )

Returns the differential entropy of an inverse gamma distribution with shape parameter alpha and rate parameter beta (in nats).

var v = entropy( 1.0, 1.0 );
// returns ~2.154

v = entropy( 4.0, 12.0 );
// returns ~1.996

v = entropy( 8.0, 2.0 );
// returns ~-0.922

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

var alpha;
var beta;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    alpha = ( randu()*10.0 ) + EPS;
    beta = ( randu()*10.0 ) + EPS;
    v = entropy( alpha, beta );
    console.log( 'α: %d, β: %d, h(X;α,β): %d', alpha.toFixed( 4 ), beta.toFixed( 4 ), v.toFixed( 4 ) );
}

C APIs

Usage

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

stdlib_base_dists_invgamma_entropy( alpha, beta )

Returns the differential entropy of an inverse gamma distribution.

double out = stdlib_base_dists_invgamma_entropy( 1.0, 1.0 );
// returns ~2.154

The function accepts the following arguments:

alpha: [in] double shape parameter.
beta: [in] double rate parameter.

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

Examples

#include "stdlib/stats/base/dists/invgamma/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 alpha;
    double beta;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        alpha = random_uniform( 0, 20 );
        beta = random_uniform( 0, 20 );
        y = stdlib_base_dists_invgamma_entropy( alpha, beta );
        printf( "α: %lf, β: %lf, h(X;α,β): %lf\n", alpha, beta, y );
    }
}