Berry-Esseen and Edgeworth approximations for the tail of an infinite sum of weighted gamma random variables

Mark S. Veillette, Murad S. Taqqu

Consider the sum $Z={\sum }_{n=1}^{\infty }{\lambda }_n({\eta }_n-\mathbb{E}{\eta }_n)$, where ${\eta }_n$ are i.i.d.~gamma random variables with shape parameter $r>0$, and the ${\lambda }_n$'s are predetermined we…