On the distribution of a product of N Gaussian random variables
Željka Stojanac , Daniel Suess , Martin Kliesch
AbstractThe 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.
|Publication size in sheets||0.5|
|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 – The International Society for Optics and Photonics, ISBN 978-1-5106-1245-7, [978-1-5106-1246-4], DOI:10.1117/12.2293183|
|Keywords in English||Gaussian random variable, Meijer G-function, Fox H-function|
|Score|| = 15.0, BookChapterSeriesAndMatConfByIndicator|
= 15.0, BookChapterSeriesAndMatConfByIndicator
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