@stdlib/stats-base-dists-truncated-normal-pdf
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    0.0.5 • Public • Published

    Probability Density Function

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    Truncated normal distribution probability density function (PDF).

    A normally distributed random variable X conditional on a < X < b is called a truncated normal distribution. The probability density function (PDF) for a truncated normal random variable is

    Probability density function (PDF) for a truncated normal distribution.

    where Phi and phi denote the cumulative distribution function and density function of the normal distribution, respectively, mu is the location and sigma > 0 is the scale parameter of the distribution. a and b are the minimum and maximum support.

    Installation

    npm install @stdlib/stats-base-dists-truncated-normal-pdf

    Usage

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

    pdf( x, a, b, mu, sigma )

    Evaluates the probability density function (PDF) for a truncated normal distribution with lower limit a, upper limit b, location parameter mu, and scale parameter sigma.

    var y = pdf( 0.9, 0.0, 1.0, 0.0, 1.0 );
    // returns ~0.7795
    
    y = pdf( 0.9, 0.0, 1.0, 0.5, 1.0 );
    // returns ~0.9617
    
    y = pdf( 0.9, -1.0, 1.0, 0.5, 1.0 );
    // returns ~0.5896
    
    y = pdf( 1.4, 0.0, 1.0, 0.0, 1.0 );
    // returns 0.0
    
    y = pdf( -0.9, 0.0, 1.0, 0.0, 1.0 );
    // returns 0.0

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

    var y = pdf( NaN, 0.0, 1.0, 0.5, 2.0 );
    // returns NaN
    
    y = pdf( 0.0, NaN, 1.0, 0.5, 2.0 );
    // returns NaN
    
    y = pdf( 0.0, 0.0, NaN, 0.5, 2.0 );
    // returns NaN
    
    y = pdf( 0.6, 0.0, 1.0, NaN, 2.0 );
    // returns NaN
    
    y = pdf( 0.6, 0.0, 1.0, 0.5, NaN );
    // returns NaN

    pdf.factory( a, b, mu, sigma )

    Returns a function for evaluating the probability density function (PDF) for a truncated normal distribution.

    var myPDF = pdf.factory( 0.0, 1.0, 0.0, 1.0 );
    var y = myPDF( 0.8 );
    // returns ~0.849
    
    myPDF = pdf.factory( 0.0, 1.0, 0.5, 1.0 );
    y = myPDF( 0.8 );
    // returns ~0.996

    Examples

    var randu = require( '@stdlib/random-base-randu' );
    var pdf = require( '@stdlib/stats-base-dists-truncated-normal-pdf' );
    
    var sigma;
    var mu;
    var a;
    var b;
    var x;
    var y;
    var i;
    
    for ( i = 0; i < 25; i++ ) {
        a = ( randu() * 80.0 ) - 40.0;
        b = a + ( randu() * 80.0 );
        x = ( randu() * 40.0 ) + a;
        mu = ( randu() * 20.0 ) - 10.0;
        sigma = ( randu() * 10.0 ) + 2.0;
        y = pdf( x, a, b, mu, sigma );
        console.log( 'x: %d, a: %d, b: %d, mu: %d, sigma: %d, f(x;a,b,mu,sigma): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), mu.toFixed( 4 ), sigma.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-truncated-normal-pdf

    Homepage

    stdlib.io

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    10

    Version

    0.0.5

    License

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    Unpacked Size

    68.4 kB

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    10

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