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Proceedings Paper

On the distribution of a product of N Gaussian random variables
Author(s): Željka Stojanac; Daniel Suess; Martin Kliesch
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Paper 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.

Paper Details

Date Published: 24 August 2017
PDF: 10 pages
Proc. SPIE 10394, Wavelets and Sparsity XVII, 1039419 (24 August 2017); doi: 10.1117/12.2275547
Show Author Affiliations
Željka Stojanac, Univ. of Cologne (Germany)
Daniel Suess, Univ. of Cologne (Germany)
Martin Kliesch, Univ. of Gdańsk (Poland)

Published in SPIE Proceedings Vol. 10394:
Wavelets and Sparsity XVII
Yue M. Lu; Dimitri Van De Ville; Manos Papadakis, Editor(s)

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