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    Probability Density Function

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    Kumaraswamy's double bounded distribution probability density function.

    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-pdf

    Usage

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

    pdf( x, a, b )

    Evaluates 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 = pdf( 0.5, 1.0, 1.0 );
    // returns 1.0
    
    y = pdf( 0.5, 2.0, 4.0 );
    // returns ~1.688
    
    y = pdf( 0.2, 2.0, 2.0 );
    // returns ~0.768
    
    y = pdf( 0.8, 4.0, 4.0 );
    // returns ~1.686
    
    y = pdf( -0.5, 4.0, 2.0 );
    // returns 0.0
    
    y = pdf( -Infinity, 4.0, 2.0 );
    // returns 0.0
    
    y = pdf( 1.5, 4.0, 2.0 );
    // returns 0.0
    
    y = pdf( +Infinity, 4.0, 2.0 );
    // returns 0.0

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

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

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

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

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

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

    pdf.factory( a, b )

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

    var mypdf = pdf.factory( 0.5, 0.5 );
    
    var y = mypdf( 0.8 );
    // returns ~0.86
    
    y = mypdf( 0.3 );
    // returns ~0.679

    Examples

    var randu = require( '@stdlib/random-base-randu' );
    var EPS = require( '@stdlib/constants-float64-eps' );
    var pdf = require( '@stdlib/stats-base-dists-kumaraswamy-pdf' );
    
    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 = pdf( x, a, b );
        console.log( 'x: %d, a: %d, b: %d, 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-pdf

    Homepage

    stdlib.io

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    98

    Version

    0.0.6

    License

    Apache-2.0

    Unpacked Size

    62.6 kB

    Total Files

    11

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    Collaborators

    • stdlib-bot
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