Numerous Pulsating Martians

    @stdlib/stats-base-dists-degenerate-logpdf
    TypeScript icon, indicating that this package has built-in type declarations

    0.0.8 • Public • Published

    Logarithm of Probability Density Function

    NPM version Build Status Coverage Status

    Degenerate distribution logarithm of probability density function (logPDF).

    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 distribution 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-logpdf

    Usage

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

    logpdf( x, mu )

    Evaluates the natural logarithm of the PDF of a degenerate distribution centered at mu.

    var y = logpdf( 2.0, 8.0 );
    // returns -Infinity
    
    y = logpdf( 8.0, 8.0 );
    // returns Infinity

    logpdf.factory( mu )

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

    var mylogpdf = logpdf.factory( 10.0 );
    
    var y = mylogpdf( 10.0 );
    // returns Infinity
    
    y = mylogpdf( 5.0 );
    // returns -Infinity
    
    y = mylogpdf( 12.0 );
    // returns -Infinity

    Examples

    var randu = require( '@stdlib/random-base-randu' );
    var round = require( '@stdlib/math-base-special-round' );
    var logpdf = require( '@stdlib/stats-base-dists-degenerate-logpdf' );
    
    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 = logpdf( x, mu );
        console.log( 'x: %d, µ: %d, ln(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.

    Community

    Chat


    Copyright

    Copyright © 2016-2022. The Stdlib Authors.

    Install

    npm i @stdlib/stats-base-dists-degenerate-logpdf

    Homepage

    stdlib.io

    DownloadsWeekly Downloads

    556

    Version

    0.0.8

    License

    Apache-2.0

    Unpacked Size

    43.2 kB

    Total Files

    12

    Last publish

    Collaborators

    • stdlib-bot
    • kgryte
    • planeshifter
    • rreusser