@stdlib/stats-base-dists-exponential-mgf
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    Moment-Generating Function

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    Exponential distribution moment-generating function (MGF).

    The moment-generating function for an exponential random variable is

    Moment-generating function (MGF) for an exponential distribution.

    where lambda > 0 is the rate parameter. For t >= lambda, the MGF is undefined.

    Installation

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

    Usage

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

    mgf( t, lambda )

    Evaluates the moment-generating function (MGF) for an exponential distribution.

    var y = mgf( 2.0, 3.0 );
    // returns 3.0
    
    y = mgf( 0.4, 1.2 );
    // returns 1.5

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

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

    If provided lambda < 0 or t >= lambda, the function returns NaN.

    var y = mgf( -2.0, -1.0 );
    // returns NaN
    
    y = mgf( 3.0, 2.0 );
    // returns NaN

    mgf.factory( lambda )

    Returns a function for evaluating the moment-generating function of an exponential distribution with parameter lambda(rate parameter).

    var mymgf = mgf.factory( 4.0 );
    var y = mymgf( 3.0 );
    // returns 4.0

    Examples

    var randu = require( '@stdlib/random-base-randu' );
    var mgf = require( '@stdlib/stats-base-dists-exponential-mgf' );
    
    var lambda;
    var t;
    var y;
    var i;
    
    for ( i = 0; i < 10; i++ ) {
        t = randu() * 10.0;
        lambda = randu() * 10.0;
        y = mgf( t, lambda );
        console.log( 'x: %d, λ: %d, M_X(t;λ): %d', t.toFixed( 4 ), lambda.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-exponential-mgf

    Homepage

    stdlib.io

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    Version

    0.0.6

    License

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    11

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