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    @stdlib/stats-base-dists-negative-binomial-pmf
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    0.0.4 • Public • Published

    Probability Mass Function

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    Negative binomial distribution probability mass function (PMF).

    The probability mass function (PMF) for a negative binomial random variable X is

    Probability mass function (PMF) for a negative binomial distribution.

    where r > 0 is the number of successes until experiment is stopped and 0 < p <= 1 is the success probability. The random variable X denotes the number of failures until the r success is reached.

    Installation

    npm install @stdlib/stats-base-dists-negative-binomial-pmf

    Usage

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

    pmf( x, r, p )

    Evaluates the probability mass function for a negative binomial distribution with number of successes until experiment is stopped r and success probability p.

    var y = pmf( 5.0, 20.0, 0.8 );
    // returns ~0.157
    
    y = pmf( 21.0, 20.0, 0.5 );
    // returns ~0.06
    
    y = pmf( 5.0, 10.0, 0.4 );
    // returns ~0.016
    
    y = pmf( 0.0, 10.0, 0.9 );
    // returns ~0.349

    While r can be interpreted as the number of successes until the experiment is stopped, the negative binomial distribution is also defined for non-integers r. In this case, r denotes shape parameter of the gamma mixing distribution.

    var y = pmf( 21.0, 15.5, 0.5 );
    // returns ~0.037
    
    y = pmf( 5.0, 7.4, 0.4 );
    // returns ~0.051

    If provided a r which is not a positive number, the function returns NaN.

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

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

    var y = pmf( NaN, 20.0, 0.5 );
    // returns NaN
    
    y = pmf( 0.0, NaN, 0.5 );
    // returns NaN
    
    y = pmf( 0.0, 20.0, NaN );
    // returns NaN

    If provided a success probability p outside of [0,1], the function returns NaN.

    var y = pmf( 2.0, 20, -1.0 );
    // returns NaN
    
    y = pmf( 2.0, 20, 1.5 );
    // returns NaN

    pmf.factory( r, p )

    Returns a function for evaluating the probability mass function (PMF) of a negative binomial distribution with number of successes until experiment is stopped r and success probability p.

    var mypmf = pmf.factory( 10, 0.5 );
    var y = mypmf( 3.0 );
    // returns ~0.03
    
    y = mypmf( 10.0 );
    // returns ~0.088

    Examples

    var randu = require( '@stdlib/random-base-randu' );
    var round = require( '@stdlib/math-base-special-round' );
    var pmf = require( '@stdlib/stats-base-dists-negative-binomial-pmf' );
    
    var i;
    var r;
    var p;
    var x;
    var y;
    
    for ( i = 0; i < 10; i++ ) {
        x = round( randu() * 30 );
        r = randu() * 50;
        p = randu();
        y = pmf( x, r, p );
        console.log( 'x: %d, r: %d, p: %d, P(X=x;r,p): %d', x, r, p.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-negative-binomial-pmf

    Homepage

    stdlib.io

    DownloadsWeekly Downloads

    39

    Version

    0.0.4

    License

    Apache-2.0

    Unpacked Size

    72.8 kB

    Total Files

    14

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