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    0.0.7 • Public • Published

    Probability Mass Function

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    Hypergeometric distribution probability mass function (PMF).

    Imagine a scenario with a population of size N, of which a subpopulation of size K can be considered successes. We draw n observations from the total population. Defining the random variable X as the number of successes in the n draws, X is said to follow a hypergeometric distribution. The probability mass function (PMF) for a hypergeometric random variable is given by

    Probability mass function (PMF) for a hypergeometric distribution.

    Installation

    npm install @stdlib/stats-base-dists-hypergeometric-pmf

    Usage

    var pmf = require( '@stdlib/stats-base-dists-hypergeometric-pmf' );

    pmf( x, N, K, n )

    Evaluates the probability mass function (PMF) for a hypergeometric distribution with parameters N (population size), K (subpopulation size), and n (number of draws).

    var y = pmf( 1.0, 8, 4, 2 );
    // returns ~0.571
    
    y = pmf( 2.0, 8, 4, 2 );
    // returns ~0.214
    
    y = pmf( 0.0, 8, 4, 2 );
    // returns ~0.214
    
    y = pmf( 1.5, 8, 4, 2 );
    // returns 0.0

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

    var y = pmf( NaN, 10, 5, 2 );
    // returns NaN
    
    y = pmf( 0.0, NaN, 5, 2 );
    // returns NaN
    
    y = pmf( 0.0, 10, NaN, 2 );
    // returns NaN
    
    y = pmf( 0.0, 10, 5, NaN );
    // returns NaN

    If provided a population size N, subpopulation size K or draws n which is not a nonnegative integer, the function returns NaN.

    var y = pmf( 2.0, 10.5, 5, 2 );
    // returns NaN
    
    y = pmf( 2.0, 10, 1.5, 2 );
    // returns NaN
    
    y = pmf( 2.0, 10, 5, -2.0 );
    // returns NaN

    If the number of draws n exceeds population size N, the function returns NaN.

    var y = pmf( 2.0, 10, 5, 12 );
    // returns NaN
    
    y = pmf( 2.0, 8, 3, 9 );
    // returns NaN

    pmf.factory( N, K, n )

    Returns a function for evaluating the probability mass function (PMF) of a hypergeometric distribution with parameters N (population size), K (subpopulation size), and n (number of draws).

    var mypmf = pmf.factory( 30, 20, 5 );
    var y = mypmf( 4.0 );
    // returns ~0.34
    
    y = mypmf( 1.0 );
    // returns ~0.029

    Examples

    var randu = require( '@stdlib/random-base-randu' );
    var round = require( '@stdlib/math-base-special-round' );
    var pmf = require( '@stdlib/stats-base-dists-hypergeometric-pmf' );
    
    var i;
    var N;
    var K;
    var n;
    var x;
    var y;
    
    for ( i = 0; i < 10; i++ ) {
        x = round( randu() * 5.0 );
        N = round( randu() * 20.0 );
        K = round( randu() * N );
        n = round( randu() * N );
        y = pmf( x, N, K, n );
        console.log( 'x: %d, N: %d, K: %d, n: %d, P(X=x;N,K,n): %d', x, N, K, n, 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-hypergeometric-pmf

    Homepage

    stdlib.io

    DownloadsWeekly Downloads

    259

    Version

    0.0.7

    License

    Apache-2.0

    Unpacked Size

    59.7 kB

    Total Files

    11

    Last publish

    Collaborators

    • stdlib-bot
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