Moment-Generating Function

Normal distribution moment-generating function (MGF).

The moment-generating function for a normal random variable is

where mu is the mean and sigma > 0 is the standard deviation.

Installation

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

Usage

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

mgf( t, mu, sigma )

Evaluates the moment-generating function (MGF) for a normal distribution with parameters mu (mean) and sigma (standard deviation).

var y = mgf( 2.0, 0.0, 1.0 );
// returns ~7.389

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

y = mgf( -1.0, 4.0, 2.0 );
// returns ~0.1353

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 sigma <= 0, the function returns NaN.

var y = mgf( 2.0, 0.0, 0.0 );
// returns NaN

y = mgf( 2.0, 0.0, -1.0 );
// returns NaN

mgf.factory( mu, sigma )

Returns a function for evaluating the moment-generating function (MGF) of a normal distribution with parameters mu and sigma.

var mymgf = mgf.factory( 4.0, 2.0 );

var y = mymgf( 1.0 );
// returns ~403.429

y = mymgf( 0.5 );
// returns ~12.182

Examples

var randu = require( '@stdlib/random-base-randu' );
var mgf = require( '@stdlib/stats-base-dists-normal-mgf' );

var sigma;
var mu;
var t;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    t = randu();
    mu = (randu() * 10.0) - 5.0;
    sigma = randu() * 20.0;
    y = mgf( t, mu, sigma );
    console.log( 't: %d, µ: %d, σ: %d, M_X(t;µ,σ): %d', t.toFixed( 4 ), mu.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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.