# @stdlib/stats-base-dists-t-entropy

0.2.2 • Public • Published

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# 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.

## Package Sidebar

### Install

`npm i @stdlib/stats-base-dists-t-entropy`

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