A note on asymptotic approximations of inverse moments of nonnegative random variables

Xiaoping Shi, Yuehua Wu and Yu Liu

Statistics & Probability Letters, 2010, vol. 80, issue 15-16, 1260-1264

Abstract: Let {Zn} be a sequence of independently distributed and nonnegative random variables and let . We show that, under mild conditions, E[(a+Xn)-[alpha]] can be asymptotically approximated by [a+E(Xn)]-[alpha] for a>0 and [alpha]>0. We further show that E{[f(Xn)]-1} can be asymptotically approximated by {f[E(Xn)]}-1 for a function f([dot operator]) satisfying certain conditions.

Date: 2010
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