Given two iid Matrix Exponential or PH distributed random variables, $X$ and $Y$, how can I find the PDF of the random variable $Z=X \cdot Y$?
2026-03-27 08:58:54.1774601934
Product of 2 Matrix Exponential or PH Random variables, $Z = X\cdot Y$
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By independence and equal distribution $$F_{X\cdot Y}(u)=\int F_X(u/x)f_X(x)dx,$$ and the result follows by differentiation w.r.t. $u$. I don't believe the Markov structure underlying Phase-type distributions can make it more explicit.