Moment-Generating Function

Rayleigh distribution moment-generating function (MGF).

The moment-generating function for a Rayleigh random variable is

where sigma > 0 is the scale parameter.

Installation

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

Usage

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

mgf( t, sigma )

Evaluates the moment-generating function for a Rayleigh distribution with scale parameter sigma.

var y = mgf( 1.0, 3.0 );
// returns ~678.508

y = mgf( 1.0, 2.0 );
// returns ~38.65

y = mgf( -1.0, 4.0 );
// returns ~-0.947

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

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

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

If provided sigma < 0, the function returns NaN.

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

mgf.factory( sigma )

Returns a function for evaluating the moment-generating function of a Rayleigh distribution with parameter sigma (scale parameter).

var myMGF = mgf.factory( 0.5 );
var y = myMGF( 1.0 );
// returns ~2.715

y = myMGF( 0.5 );
// returns ~1.888

Examples

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

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

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