README.md

About stdlib...

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Entropy

Beta distribution differential entropy.

The differential entropy for a beta random variable is

$$h\left( X \right) = \ln(\mathop{\mathrm{Beta}}(\alpha,\beta)) - (\alpha-1)\psi(\alpha) - (\beta-1)\psi(\beta) + (\alpha+\beta-2)\psi(\alpha+\beta)$$

where α > 0 is the first shape parameter and β > 0 is the second shape parameter.

Usage

import entropy from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-beta-entropy@deno/mod.js';

entropy( alpha, beta )

Returns the differential entropy of a beta distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var v = entropy( 1.0, 1.0 );
// returns 0.0

v = entropy( 4.0, 12.0 );
// returns ~-0.869

v = entropy( 8.0, 2.0 );
// returns ~-0.795

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

import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@deno/mod.js';
import EPS from 'https://cdn.jsdelivr.net/gh/stdlib-js/constants-float64-eps@deno/mod.js';
import entropy from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-beta-entropy@deno/mod.js';

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 ) );
}

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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.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.