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    @stdlib/stats-base-dists-binomial-mgf
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    0.0.7 • Public • Published

    Moment-Generating Function

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    Binomial distribution moment-generating function (MGF).

    The moment-generating function for a binomial random variable is

    Moment-generating function (MGF) for a binomial distribution.

    where the nonnegative integer n is the number of trials and 0 <= p <= 1 is the success probability.

    Installation

    npm install @stdlib/stats-base-dists-binomial-mgf

    Usage

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

    mgf( t, n, p )

    Evaluates the moment-generating function for a binomial distribution with number of trials n and success probability p.

    var y = mgf( 0.5, 20, 0.2 );
    // returns ~11.471
    
    y = mgf( 5.0, 20, 0.2 );
    // returns ~4.798e29
    
    y = mgf( 0.9, 10, 0.4 );
    // returns ~99.338
    
    y = mgf( 0.0, 10, 0.4 );
    // returns 1.0

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

    var y = mgf( NaN, 20, 0.5 );
    // returns NaN
    
    y = mgf( 0.0, NaN, 0.5 );
    // returns NaN
    
    y = mgf( 0.0, 20, NaN );
    // returns NaN

    If provided a number of trials n which is not a nonnegative integer, the function returns NaN.

    var y = mgf( 0.2, 1.5, 0.5 );
    // returns NaN
    
    y = mgf( 0.2, -2.0, 0.5 );
    // returns NaN

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

    var y = mgf( 0.2, 20, -1.0 );
    // returns NaN
    
    y = mgf( 0.2, 20, 1.5 );
    // returns NaN

    mgf.factory( n, p )

    Returns a function for evaluating the moment-generating function of a binomial distribution with number of trials n and success probability p.

    var myMGF = mgf.factory( 10, 0.5 );
    
    var y = myMGF( 0.3 );
    // returns ~5.013

    Examples

    var randu = require( '@stdlib/random-base-randu' );
    var round = require( '@stdlib/math-base-special-round' );
    var mgf = require( '@stdlib/stats-base-dists-binomial-mgf' );
    
    var n;
    var p;
    var t;
    var y;
    var i;
    
    for ( i = 0; i < 10; i++ ) {
        t = round( randu() * 5.0 );
        n = round( randu() * 10.0 );
        p = randu();
        y = mgf( t, n, p );
        console.log( 't: %d, n: %d, p: %d, M_X(t;n,p): %d', t, n, 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 © 2016-2022. The Stdlib Authors.

    Install

    npm i @stdlib/stats-base-dists-binomial-mgf

    Homepage

    stdlib.io

    DownloadsWeekly Downloads

    104

    Version

    0.0.7

    License

    Apache-2.0

    Unpacked Size

    44.4 kB

    Total Files

    11

    Last publish

    Collaborators

    • stdlib-bot
    • kgryte
    • planeshifter
    • rreusser