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    0.0.6 • Public • Published

    Logarithm of Probability Density Function

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    Evaluate the natural logarithm of the probability density function for a Kumaraswamy's double bounded distribution.

    The probability density function (PDF) for a Kumaraswamy's double bounded random variable is

    Probability density function (PDF) for a Kumaraswamy's double bounded distribution.

    where a > 0 is the first shape parameter and b > 0 is the second shape parameter.

    Installation

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

    Usage

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

    logpdf( x, a, b )

    Evaluates the natural logarithm of the probability density function (PDF) for a Kumaraswamy's double bounded distribution with parameters a (first shape parameter) and b (second shape parameter).

    var y = logpdf( 0.5, 1.0, 1.0 );
    // returns 0.0
    
    y = logpdf( 0.5, 2.0, 4.0 );
    // returns ~0.523
    
    y = logpdf( 0.2, 2.0, 2.0 );
    // returns ~-0.264
    
    y = logpdf( 0.8, 4.0, 4.0 );
    // returns ~0.522
    
    y = logpdf( -0.5, 4.0, 2.0 );
    // returns -Infinity
    
    y = logpdf( -Infinity, 4.0, 2.0 );
    // returns -Infinity
    
    y = logpdf( 1.5, 4.0, 2.0 );
    // returns -Infinity
    
    y = logpdf( +Infinity, 4.0, 2.0 );
    // returns -Infinity

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

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

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

    var y = logpdf( 2.0, -1.0, 0.5 );
    // returns NaN
    
    y = logpdf( 2.0, 0.0, 0.5 );
    // returns NaN

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

    var y = logpdf( 2.0, 0.5, -1.0 );
    // returns NaN
    
    y = logpdf( 2.0, 0.5, 0.0 );
    // returns NaN

    logpdf.factory( a, b )

    Returns a function for evaluating the natural logarithm of the probability density function (PDF) for a Kumaraswamy's double bounded distribution with parameters a (first shape parameter) and b (second shape parameter).

    var mylogpdf = logpdf.factory( 0.5, 0.5 );
    
    var y = mylogpdf( 0.8 );
    // returns ~-0.151
    
    y = mylogpdf( 0.3 );
    // returns ~-0.388

    Notes

    • In virtually all cases, using the logpdf or logcdf functions is preferable to manually computing the logarithm of the pdf or cdf, respectively, since the latter is prone to overflow and underflow.

    Examples

    var randu = require( '@stdlib/random-base-randu' );
    var EPS = require( '@stdlib/constants-float64-eps' );
    var logpdf = require( '@stdlib/stats-base-dists-kumaraswamy-logpdf' );
    
    var a;
    var b;
    var x;
    var y;
    var i;
    
    for ( i = 0; i < 10; i++ ) {
        x = randu();
        a = ( randu()*5.0 ) + EPS;
        b = ( randu()*5.0 ) + EPS;
        y = logpdf( x, a, b );
        console.log( 'x: %d, a: %d, b: %d, ln(f(x;a,b)): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.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-kumaraswamy-logpdf

    Homepage

    stdlib.io

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    84

    Version

    0.0.6

    License

    Apache-2.0

    Unpacked Size

    64.3 kB

    Total Files

    11

    Last publish

    Collaborators

    • stdlib-bot
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