On the distribution of a product of N Gaussian random variables

Željka Stojanac; Daniel Suess; Martin Kliesch

doi:10.1117/12.2275547

24 August 2017 On the distribution of a product of N Gaussian random variables

Željka Stojanac, Daniel Suess, Martin Kliesch

Proceedings Volume 10394, Wavelets and Sparsity XVII; 1039419 (2017) https://doi.org/10.1117/12.2275547
Event: SPIE Optical Engineering + Applications, 2017, San Diego, California, United States

Abstract

The product of Gaussian random variables appears naturally in many applications in probability theory and statistics. It has been known that the distribution of a product of N such variables can be expressed in terms of a Meijer G-function. Here, we compute a similar representation for the corresponding cumulative distribution function (CDF) and provide a power-log series expansion of the CDF based on the theory of the more general Fox H-functions. Numerical computations show that for small values of the argument the CDF of products of Gaussians is well approximated by the lowest orders of this expansion. Analogous results are also shown for the absolute value as well as the square of such products of N Gaussian random variables. For the latter two settings, we also compute the moment generating functions in terms of Meijer G-functions.

Conference Presentation

Citation Download Citation

Željka Stojanac, Daniel Suess, and Martin Kliesch "On the distribution of a product of N Gaussian random variables", Proc. SPIE 10394, Wavelets and Sparsity XVII, 1039419 (24 August 2017); https://doi.org/10.1117/12.2275547

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available