Entropy

Lévy distribution differential entropy.

The differential entropy (in nats) for a Lévy random variable with location μ and scale c > 0 is

where γ is the Euler-Mascheroni constants.

Installation

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

Usage

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

entropy( mu, c )

Returns the differential entropy for a Lévy distribution with location parameter mu and scale parameter c (in nats).

var y = entropy( 2.0, 1.0 );
// returns ~3.324

y = entropy( 0.0, 1.0 );
// returns ~3.324

y = entropy( -1.0, 4.0 );
// returns ~4.711

If provided NaN as any argument, the function returns NaN.

var y = entropy( NaN, 1.0 );
// returns NaN

y = entropy( 0.0, NaN );
// returns NaN

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

var y = entropy( 0.0, 0.0 );
// returns NaN

y = entropy( 0.0, -1.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random-base-randu' );
var entropy = require( '@stdlib/stats-base-dists-levy-entropy' );

var mu;
var c;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    mu = ( randu()*10.0 ) - 5.0;
    c = randu() * 20.0;
    y = entropy( mu, c );
    console.log( 'µ: %d, c: %d, h(X;µ,c): %d', mu.toFixed( 4 ), c.toFixed( 4 ), y.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.