Moment-Generating Function

Geometric distribution moment-generating function (MGF).

The moment-generating function for a geometric random variable is

where 0 < p <= 1 is the success probability. For t >= -ln(1-p), the MGF is not defined.

Installation

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

Usage

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

mgf( t, p )

Evaluates the moment-generating function (MGF) of a geometric distribution with success probability p.

var y = mgf( 0.2, 0.5 );
// returns ~1.569

y = mgf( 0.4, 0.5 );
// returns ~2.936

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

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

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

If provided a success probability p outside of the interval [0,1], the function returns NaN.

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

y = mgf( 0.2, 2.0 );
// returns NaN

If t >= -ln(1-p), the function returns NaN.

var y = mgf( 0.8, 0.5 );
// returns NaN

mgf.factory( p )

Returns a function for evaluating the moment-generating function of a geometric distribution with parameter p (success probability).

var mymgf = mgf.factory( 0.8 );
var y = mymgf( -0.2 );
// returns ~0.783

Examples

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

var p;
var t;
var y;
var i;

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