@stdlib/stats-base-dists-degenerate-pdf
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    0.0.7 • Public • Published

    Probability Density Function

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    Degenerate distribution probability density function (PDF).

    Strictly speaking, as a discrete distribution, a degenerate has no probability density function (PDF). Extending the notion of a PDF, we conceptualize the PDF of a degenerate as an infinitely tall spike centered at mu. More formally,

    Probability density function (PDF) for a degenerate distribution.

    where delta is the Dirac delta function.

    Dirac delta function.

    Installation

    npm install @stdlib/stats-base-dists-degenerate-pdf

    Usage

    var pdf = require( '@stdlib/stats-base-dists-degenerate-pdf' );

    pdf( x, mu )

    Evaluates the PDF of a degenerate distribution centered at mu.

    var y = pdf( 2.0, 8.0 );
    // returns 0.0
    
    y = pdf( 8.0, 8.0 );
    // returns Infinity

    pdf.factory( mu )

    Returns a function for evaluating the PDF of a degenerate distribution centered at mu.

    var mypdf = pdf.factory( 10.0 );
    
    var y = mypdf( 10.0 );
    // returns Infinity
    
    y = mypdf( 5.0 );
    // returns 0.0
    
    y = mypdf( 12.0 );
    // returns 0.0

    Examples

    var randu = require( '@stdlib/random-base-randu' );
    var round = require( '@stdlib/math-base-special-round' );
    var pdf = require( '@stdlib/stats-base-dists-degenerate-pdf' );
    
    var mu;
    var x;
    var y;
    var i;
    
    for ( i = 0; i < 100; i++ ) {
        x = round( randu()*5.0 );
        mu = round( randu()*5.0 );
        y = pdf( x, mu );
        console.log( 'x: %d, µ: %d, f(x;µ): %d', x, mu, y );
    }

    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-degenerate-pdf

    Homepage

    stdlib.io

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    704

    Version

    0.0.7

    License

    Apache-2.0

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    55.9 kB

    Total Files

    12

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    Collaborators

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