On the distribution of a product of N Gaussian random variables

Željka Stojanac , Daniel Suess , Martin Kliesch

Abstract

The product of Gaussian random variables appears naturally in many applications in probability theory andstatistics. It has been known that the distribution of a product of N such variables can be expressed in terms ofa Meijer G-function. Here, we compute a similar representation for the corresponding cumulative distributionfunction (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 forthe absolute value as well as the square of such products of N Gaussian random variables. For the latter twosettings, we also compute the moment generating functions in terms of Meijer G-functions.
Author Željka Stojanac
Željka Stojanac,,
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, Daniel Suess
Daniel Suess,,
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, Martin Kliesch (FMPI / ITPA)
Martin Kliesch,,
- Institute of Theoretical Physics and Astrophysics
Pages1-10
Publication size in sheets0.5
Book Lu Yue M., De Ville Dimitri Van, Papadakis Manos (eds.): Wavelets and Sparsity XVII : 6-9 August 2017, San Diego, California, United States, Proceedings of SPIE: The International Society for Optical Engineering, no. 10394, 2017, SPIE, ISBN 978-1-5106-1245-7, [978-1-5106-1246-4], DOI:10.1117/12.2293183
Keywords in EnglishGaussian random variable, Meijer G-function, Fox H-function
DOIDOI:10.1117/12.2275547
Languageen angielski
Score (nominal)15
ScoreMinisterial score = 15.0, BookChapterSeriesAndMatConfByIndicator
Ministerial score (2013-2016) = 15.0, BookChapterSeriesAndMatConfByIndicator
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