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    @stdlib/stats-base-dists-invgamma-entropy
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    0.0.7 • Public • Published

    Entropy

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    Inverse gamma distribution differential entropy.

    The differential entropy (in nats) for an inverse gamma random variable is

    Differential entropy for an inverse gamma distribution.

    where α > 0 is the shape parameter, β > 0 is the rate parameter, Γ and denotes the gamma and Ψ the digamma function.

    Installation

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

    Usage

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

    entropy( alpha, beta )

    Returns the differential entropy of an inverse gamma distribution with shape parameter alpha and rate parameter beta (in nats).

    var v = entropy( 1.0, 1.0 );
    // returns ~2.154
    
    v = entropy( 4.0, 12.0 );
    // returns ~1.996
    
    v = entropy( 8.0, 2.0 );
    // returns ~-0.922

    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

    var randu = require( '@stdlib/random-base-randu' );
    var EPS = require( '@stdlib/constants-float64-eps' );
    var entropy = require( '@stdlib/stats-base-dists-invgamma-entropy' );
    
    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 ) );
    }

    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.

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    License

    See LICENSE.

    Copyright

    Copyright © 2016-2022. The Stdlib Authors.

    Install

    npm i @stdlib/stats-base-dists-invgamma-entropy

    Homepage

    stdlib.io

    DownloadsWeekly Downloads

    113

    Version

    0.0.7

    License

    Apache-2.0

    Unpacked Size

    35.2 kB

    Total Files

    10

    Last publish

    Collaborators

    • stdlib-bot
    • kgryte
    • planeshifter
    • rreusser