# @stdlib/stats-base-dists-gamma-entropy 0.1.0 • Public • Published

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# Entropy

Gamma distribution differential entropy.

The differential entropy (in nats) for a gamma random variable with shape parameter α > 0 and rate parameter β > 0 is

where Γ and Ψ denote the gamma and digamma function, respectively.

## Installation

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

## Usage

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

#### entropy( alpha, beta )

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

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

v = entropy( 4.0, 12.0 );
// returns ~-0.462

v = entropy( 8.0, 2.0 );
// returns ~1.723

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-gamma-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 ) );
}

## 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 ## Package Sidebar

### Install

npm i @stdlib/stats-base-dists-gamma-entropy

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