Moment-Generating Function

Gumbel distribution moment-generating function (MGF).

The moment-generating function for a Gumbel random variable is

where mu is the location parameter and beta > 0 is the scale parameter.

Installation

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

Usage

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

mgf( t, mu, beta )

Evaluates the moment-generating function (MGF) for a Gumbel distribution with parameters mu (location parameter) and beta > 0 (scale parameter).

var y = mgf( -1.0, 0.0, 3.0 );
// returns 6.0

y = mgf( 0.1, 0.0, 3.0 );
// returns ~1.298

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

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 t >= 1/beta, the function returns NaN.

var y = mgf( 0.8, 0.0, 2.0 );
// returns NaN

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

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

y = mgf( 0.5, 0.0, 0.0 );
// returns NaN

mgf.factory( mu, beta )

Returns a function for evaluating the moment-generating function of a Gumbel distribution with parameters mu (location parameter) and beta > 0 (scale parameter).

var myMGF = mgf.factory( 0.0, 2.0 );
var y = myMGF( 0.2 );
// returns ~1.489

y = myMGF( -1.0 );
// returns 2.0

Examples

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

var beta;
var mu;
var t;
var y;
var i;

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