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    @stdlib/stats-base-dists-erlang-logpdf
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    0.0.7 • Public • Published

    Logarithm of Probability Density Function

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    Evaluate the natural logarithm of the probability density function (PDF) for an Erlang distribution.

    The probability density function (PDF) for an Erlang random variable is

    Probability density function (PDF) for an Erlang distribution.

    where k is the shape parameter and lambda is the rate parameter.

    Installation

    npm install @stdlib/stats-base-dists-erlang-logpdf

    Usage

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

    logpdf( x, k, lambda )

    Evaluates the natural logarithm of the probability density function (PDF) for an Erlang distribution with parameters k (shape parameter) and lambda (rate parameter).

    var y = logpdf( 0.1, 1, 1.0 );
    // returns ~-0.1
    
    y = logpdf( 0.5, 2, 2.5 );
    // returns ~-0.111
    
    y = logpdf( -1.0, 4, 2.0 );
    // returns -Infinity

    If provided NaN as any argument, the function returns NaN.

    var y = logpdf( NaN, 1, 1.0 );
    // returns NaN
    
    y = logpdf( 0.0, NaN, 1.0 );
    // returns NaN
    
    y = logpdf( 0.0, 1, NaN );
    // returns NaN

    If not provided a nonnegative integer for k, the function returns NaN.

    var y = logpdf( 2.0, -2, 0.5 );
    // returns NaN
    
    y = logpdf( 2.0, 0.5, 0.5 );
    // returns NaN

    If provided k = 0, the function evaluates the logarithm of the PDF of a degenerate distribution centered at 0.

    var y = logpdf( 2.0, 0.0, 2.0 );
    // returns -Infinity
    
    y = logpdf( 0.0, 0.0, 2.0 );
    // returns Infinity

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

    var y = logpdf( 2.0, 1, 0.0 );
    // returns NaN
    
    y = logpdf( 2.0, 1, -1.0 );
    // returns NaN

    logpdf.factory( k, lambda )

    Returns a function for evaluating the PDF for an Erlang distribution with parameters k (shape parameter) and lambda (rate parameter).

    var mylogpdf = logpdf.factory( 3, 1.5 );
    
    var y = mylogpdf( 1.0 );
    // returns ~-0.977
    
    y = mylogpdf( 4.0 );
    // returns ~-2.704

    Examples

    var randu = require( '@stdlib/random-base-randu' );
    var round = require( '@stdlib/math-base-special-round' );
    var logpdf = require( '@stdlib/stats-base-dists-erlang-logpdf' );
    
    var lambda;
    var k;
    var x;
    var y;
    var i;
    
    for ( i = 0; i < 20; i++ ) {
        x = randu() * 10.0;
        k = round( randu() * 10.0 );
        lambda = randu() * 5.0;
        y = logpdf( x, k, lambda );
        console.log( 'x: %d, k: %d, λ: %d, ln(f(x;k,λ)): %d', x.toFixed( 4 ), k, lambda.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.

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    License

    See LICENSE.

    Copyright

    Copyright © 2016-2022. The Stdlib Authors.

    Install

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

    Homepage

    stdlib.io

    DownloadsWeekly Downloads

    77

    Version

    0.0.7

    License

    Apache-2.0

    Unpacked Size

    42.9 kB

    Total Files

    11

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    Collaborators

    • stdlib-bot
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