Moment-Generating Function

Gamma distribution moment-generating function (MGF).

The moment-generating function for a gamma random variable is

where alpha is the shape parameter and beta is the rate parameter. For t >= beta, the MGF is not defined.

Installation

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

Usage

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

mgf( t, alpha, beta )

Evaluates the moment-generating function (MGF) for a gamma distribution with parameters alpha (shape parameter) and beta (rate parameter).

var y = mgf( 0.5, 0.5, 1.0 );
// returns ~1.414

y = mgf( 0.1, 1.0, 1.0 );
// returns ~1.111

y = mgf( -1.0, 4.0, 2.0 );
// returns ~0.198

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

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

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

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

If provided t >= beta, the function returns NaN.

var y = mgf( 2.0, 4.0, 1.0 );
// returns NaN

If provided alpha < 0, the function returns NaN.

var y = mgf( 2.0, -0.5, 1.0 );
// returns NaN

If provided beta <= 0, the function returns NaN.

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

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

mgf.factory( alpha, beta )

Return a function for evaluating the MGF of a gamma distribution with parameters alpha (shape parameter) and beta (rate parameter).

var mymgf = mgf.factory( 3.0, 1.5 );

var y = mymgf( 1.0 );
// returns ~27.0

y = mymgf( 0.5 );
// returns ~3.375

Examples

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

var a;
var b;
var t;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    t = randu();
    a = randu() * 5.0;
    b = a + (randu() * 5.0);
    v = mgf( t, a, b );
    console.log( 't: %d, a: %d, b: %d, M_X(t;a,b): %d', t.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), v.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.