Entropy

Student's t distribution differential entropy.

The differential entropy (in nats) for a Student's t random variable with degrees of freedom ν is

where Β and ψ denote the beta and digamma functions, respectively.

Installation

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

Usage

var entropy = require( '@stdlib/stats-base-dists-t-entropy' );

entropy( v )

Returns the differential entropy of a Student's t distribution with degrees of freedom v (in nats).

var y = entropy( 9.0 );
// returns ~1.533

y = entropy( 3.5 );
// returns ~1.721

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

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

y = entropy( 0.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var entropy = require( '@stdlib/stats-base-dists-t-entropy' );

var v;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    v = randu() * 20.0;
    y = entropy( v );
    console.log( 'v: %d, h(X,v): %d', v.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.