On the distribution-tail of the product of gamma random variables - Kamarauskas, Ričardas; Šiaulys, Jonas (Nonlinear Analysis: Modelling and Control, 2024)
In this paper, we consider the product Πn := ∏nk=1 ξk of n independent identically distributed gamma random variables ξ1, ξ2, . . . , ξn. We derive an asymptotic formula for the survival probability P(Πn > x) as x -> ∞ with the first two remaining terms.
Keywords: gamma distribution; tail distribution function; saddle-point method; asymptotic functions; product of random variables