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    @stdlib/stats-base-dists-frechet-pdf
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    0.0.4 • Public • Published

    Probability Density Function

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    Fréchet distribution probability density function.

    The probability density function for a Fréchet random variable is

    Probability density function for a Fréchet distribution.

    where alpha > 0 is the shape, s > 0 the scale and m the location parameter.

    Installation

    npm install @stdlib/stats-base-dists-frechet-pdf

    Usage

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

    pdf( x, alpha, s, m )

    Evaluates the probability density function (PDF) for a Fréchet distribution with shape alpha, scale s, and location m at a value x.

    var y = pdf( 10.0, 2.0, 3.0, 5.0 );
    // returns ~0.1
    
    y = pdf( -3.0, 1.0, 2.0, -4.0 );
    // returns ~0.271
    
    y = pdf( 0.0, 2.0, 1.0, -1.0 );
    // returns ~0.736

    If provided x <= m, the function returns 0.

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

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

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

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

    var y = pdf( 2.0, -0.1, 1.0, 1.0 );
    // returns NaN
    
    y = pdf( 2.0, 0.0, 1.0, 1.0 );
    // returns NaN

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

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

    pdf.factory( alpha, s, m )

    Returns a function for evaluating the probability density function of a Fréchet distribution with shape alpha, scale s, and location m.

    var mypdf = pdf.factory( 3.0, 3.0, 5.0 );
    
    var y = mypdf( 10.0 );
    // returns ~0.104
    
    y = mypdf( 7.0 );
    // returns ~0.173

    Examples

    var randu = require( '@stdlib/random-base-randu' );
    var pdf = require( '@stdlib/stats-base-dists-frechet-pdf' );
    
    var alpha;
    var m;
    var s;
    var x;
    var y;
    var i;
    
    for ( i = 0; i < 100; i++ ) {
        alpha = randu() * 10.0;
        x = randu() * 10.0;
        s = randu() * 10.0;
        m = randu() * 10.0;
        y = pdf( x, alpha, s, m );
        console.log( 'x: %d, α: %d, s: %d, m: %d, f(x;α,s,m): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), s.toFixed( 4 ), m.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 © 2016-2021. The Stdlib Authors.

    Install

    npm i @stdlib/stats-base-dists-frechet-pdf

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    12

    Version

    0.0.4

    License

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    Unpacked Size

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    12

    Homepage

    stdlib.io

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