@stdlib/stats-base-dists-logistic-mgf
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    0.0.5 • Public • Published

    Moment-Generating Function

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    Logistic distribution moment-generating function (MGF).

    The moment-generating function for a logistic random variable is

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

    for st ∈ (-1,1), where mu is the location parameter and s is the scale parameter. In above equation, B denotes the Beta function. For st outside the interval (-1,1), the function is not defined.

    Installation

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

    Usage

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

    mgf( t, mu, s )

    Evaluates the logarithm of the moment-generating function (MGF) for a logistic distribution with parameters mu (location parameter) and s (scale parameter).

    var y = mgf( 0.9, 0.0, 1.0 );
    // returns ~9.15
    
    y = mgf( 0.1, 4.0, 4.0 );
    // returns ~1.971
    
    y = mgf( -0.2, 4.0, 4.0 );
    // returns ~1.921

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

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

    If provided s < 0 or abs( s * t ) > 1, the function returns NaN.

    var y = mgf( 0.5, 0.0, -1.0 );
    // returns NaN
    
    y = mgf( 0.5, 0.0, 4.0 );
    // returns NaN

    mgf.factory( mu, s )

    Returns a function for evaluating the moment-generating function (MGF) of a logistic distribution with parameters mu (location parameter) and s (scale parameter).

    var mymgf = mgf.factory( 10.0, 0.5 );
    
    var y = mymgf( 0.5 );
    // returns ~164.846
    
    y = mymgf( 2.0 );
    // returns Infinity

    Examples

    var randu = require( '@stdlib/random-base-randu' );
    var mgf = require( '@stdlib/stats-base-dists-logistic-mgf' );
    
    var mu;
    var s;
    var t;
    var y;
    var i;
    
    for ( i = 0; i < 10; i++ ) {
        t = randu();
        mu = (randu() * 10.0) - 5.0;
        s = randu() * 2.0;
        y = mgf( t, mu, s );
        console.log( 't: %d, µ: %d, s: %d, M_X(t;µ,s): %d', t.toFixed( 4 ), mu.toFixed( 4 ), s.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-logistic-mgf

    Homepage

    stdlib.io

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    4

    Version

    0.0.5

    License

    Apache-2.0

    Unpacked Size

    57.5 kB

    Total Files

    11

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    Collaborators

    • stdlib-bot
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    • rreusser