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    @stdlib/stats-base-dists-rayleigh-mgf
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    0.0.6 • Public • Published

    Moment-Generating Function

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    Rayleigh distribution moment-generating function (MGF).

    The moment-generating function for a Rayleigh random variable is

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

    where sigma > 0 is the scale parameter.

    Installation

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

    Usage

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

    mgf( t, sigma )

    Evaluates the moment-generating function for a Rayleigh distribution with scale parameter sigma.

    var y = mgf( 1.0, 3.0 );
    // returns ~678.508
    
    y = mgf( 1.0, 2.0 );
    // returns ~38.65
    
    y = mgf( -1.0, 4.0 );
    // returns ~-0.947

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

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

    If provided sigma < 0, the function returns NaN.

    var y = mgf( 0.5, -1.0 );
    // returns NaN

    mgf.factory( sigma )

    Returns a function for evaluating the moment-generating function of a Rayleigh distribution with parameter sigma (scale parameter).

    var myMGF = mgf.factory( 0.5 );
    var y = myMGF( 1.0 );
    // returns ~2.715
    
    y = myMGF( 0.5 );
    // returns ~1.888

    Examples

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

    Install

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

    Homepage

    stdlib.io

    DownloadsWeekly Downloads

    90

    Version

    0.0.6

    License

    Apache-2.0

    Unpacked Size

    60.1 kB

    Total Files

    11

    Last publish

    Collaborators

    • stdlib-bot
    • kgryte
    • planeshifter
    • rreusser