From Event: SPIE Optical Engineering + Applications, 2017
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.
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 (Presented at SPIE Optical Engineering + Applications: August 08, 2017; Published: 24 August 2017); https://doi.org/10.1117/12.2275547.
Conference Presentations are recordings of oral presentations given at SPIE conferences and published as part of the conference proceedings. They include the speaker's narration along with a video recording of the presentation slides and animations. Many conference presentations also include full-text papers. Search and browse our growing collection of more than 12,000 conference presentations, including many plenary and keynote presentations.