On computing distributions of products of non-negative independent random variables
Probability
2018-02-13 v2
Abstract
We introduce a new functional representation of probability density functions (PDFs) of non-negative random variables via a product of a monomial factor and linear combinations of decaying exponentials with complex exponents. This approximate representation of PDFs is obtained for any finite, user-selected accuracy. Using a fast algorithm involving Hankel matrices, we develop a general numerical method for computing the PDF of the sums, products, or quotients of any number of non-negative random variables yielding the result in the same type of functional representation. We present several examples to demonstrate the accuracy of the approach.
Keywords
Cite
@article{arxiv.1707.07762,
title = {On computing distributions of products of non-negative independent random variables},
author = {Gregory Beylkin and Lucas Monzon and Ignas Satkauskas},
journal= {arXiv preprint arXiv:1707.07762},
year = {2018}
}