Moment-Generating Function

Degenerate distribution moment-generating function (MGF).

The moment-generating function for a degenerate random variable is

upper M Subscript upper X Baseline left-parenthesis t right-parenthesis colon equals e Superscript mu t

where mu is the distribution mean.

Usage

var mgf = require( '@stdlib/math/base/dists/degenerate/mgf' );

mgf( t, mu )

Evaluates the moment-generating function (MGF) of a degenerate distribution with parameter mu (mean).

var y = mgf( 1.0, 1.0 );
// returns ~2.718

y = mgf( 2.0, 3.0 );
// returns ~403.429

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

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

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

mgf.factory( mu )

Returns a function for evaluating the moment-generating function of a degenerate distribution with parameter mu (mean).

var mymgf = mgf.factory( 10.0 );

var y = mymgf( 0.1 );
// returns ~2.718

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var mgf = require( '@stdlib/math/base/dists/degenerate/mgf' );

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

for ( i = 0; i < 100; i++ ) {
    t = round( randu()*5.0 );
    mu = round( randu()*5.0 );
    y = mgf( t, mu );
    console.log( 'x: %d, µ: %d, M_X(t;µ): %d', t, mu, y );
}