# 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/math/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/math/float64-eps' );
var entropy = require( '@stdlib/math/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 ) );
}