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    @stdlib/stats-base-dists-pareto-type1-pdf
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    0.0.7 • Public • Published

    Probability Density Function

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    Pareto (Type I) distribution probability density function (PDF).

    The probability density function (PDF) for a Pareto (Type I) random variable is

    Probability density function (PDF) for a Pareto (Type I) distribution.

    where alpha > 0 is the shape parameter and beta > 0 is the scale parameter.

    Installation

    npm install @stdlib/stats-base-dists-pareto-type1-pdf

    Usage

    var pdf = require( '@stdlib/stats-base-dists-pareto-type1-pdf' );

    pdf( x, alpha, beta )

    Evaluates the probability density function (PDF) for a Pareto (Type I) distribution with parameters alpha (shape parameter) and beta (scale parameter).

    var y = pdf( 4.0, 1.0, 1.0 );
    // returns ~0.063
    
    y = pdf( 20.0, 1.0, 10.0 );
    // returns 0.025
    
    y = pdf( 7.0, 2.0, 6.0 );
    // returns ~0.21
    
    y = pdf( 7.0, 6.0, 3.0 );
    // returns ~0.005
    
    y = pdf( 1.0, 4.0, 2.0 );
    // returns 0.0
    
    y = pdf( 1.5, 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 alpha <= 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 beta <= 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( alpha, beta )

    Returns a function for evaluating the probability density function (PDF) (CDF) of a Pareto (Type I) distribution with parameters alpha (shape parameter) and beta (scale parameter).

    var mypdf = pdf.factory( 0.5, 0.5 );
    var y = mypdf( 0.8 );
    // returns ~0.494
    
    y = mypdf( 2.0 );
    // returns ~0.125

    Examples

    var randu = require( '@stdlib/random-base-randu' );
    var pdf = require( '@stdlib/stats-base-dists-pareto-type1-pdf' );
    
    var alpha;
    var beta;
    var x;
    var y;
    var i;
    
    for ( i = 0; i < 10; i++ ) {
        x = randu() * 8.0;
        alpha = randu() * 4.0;
        beta = randu() * 4.0;
        y = pdf( x, alpha, beta );
        console.log( 'x: %d, α: %d, β: %d, f(x;α,β): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.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-pareto-type1-pdf

    Homepage

    stdlib.io

    DownloadsWeekly Downloads

    115

    Version

    0.0.7

    License

    Apache-2.0

    Unpacked Size

    48.2 kB

    Total Files

    11

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    Collaborators

    • stdlib-bot
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