Entropy

Erlang distribution differential entropy.

The differential entropy for an Erlang random variable with shape k and rate λ is

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

Installation

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

Usage

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

entropy( k, lambda )

Returns the differential entropy of an Erlang distribution with parameters shape k and rate lambda (in nats).

var v = entropy( 1, 1.0 );
// returns 1.0

v = entropy( 4, 12.0 );
// returns ~-0.462

v = entropy( 8, 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 not provided a positive integer for k, the function returns NaN.

var v = entropy( 1.8, 1.0 );
// returns NaN

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

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

var v = entropy( 2, 0.0 );
// returns NaN

v = entropy( 2, -1.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var EPS = require( '@stdlib/constants-float64-eps' );
var entropy = require( '@stdlib/stats-base-dists-erlang-entropy' );

var lambda;
var k;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    k = round( randu()*10.0 );
    lambda = ( randu()*10.0 ) + EPS;
    v = entropy( k, lambda );
    console.log( 'k: %d, λ: %d, h(X;k,λ): %d', k.toFixed( 4 ), lambda.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

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.