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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.