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About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

Entropy

NPM version Build Status Coverage Status

Erlang distribution differential entropy.

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

$$h\left( X \right) = (1\,-\,k)\psi (k)\,+\,\ln \left[{\frac {\Gamma (k)}{\lambda }}\right]\,+\,k$$

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

Usage

import entropy from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-erlang-entropy@esm/index.mjs';

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

<!DOCTYPE html>
<html lang="en">
<body>
<script type="module">

import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@esm/index.mjs';
import round from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-round@esm/index.mjs';
import EPS from 'https://cdn.jsdelivr.net/gh/stdlib-js/constants-float64-eps@esm/index.mjs';
import entropy from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-erlang-entropy@esm/index.mjs';

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 ) );
}

</script>
</body>
</html>

Notice

This package is part of stdlib, a standard library 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.

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.