A Note on the Inverse Moment for the Non Negative Random Variables

Shuhe Hu, Xinghui Wang, Wenzhi Yang and Xuejun Wang

Communications in Statistics - Theory and Methods, 2014, vol. 43, issue 8, 1750-1757

Abstract: Let {Zn} be a sequence of non negative random variables satisfying a Rosenthal-type inequality and Xn=Mn-1∑i=1nZi$X_n=M_n^{-1}\sum \nolimits _{i=1}^n Z_i$, where {Mn} is a sequence of positive real numbers. By using the Rosenthal-type inequality, the inverse moment E(a + Xn)− α can be asymptotically approximated by (a + EXn)− α for all a > 0 and α > 0. Furthermore, we show that E[f(Xn)]− 1 can be asymptotically approximated by [f(EXn)]− 1 for a function f( · ) satisfying certain conditions. Our results generalize and improve some corresponding results, which can allow immediate applications to compute the inverse moments for the non negative random variables whose distributions are such as Binomial distribution, Poisson distribution, Gamma distribution, etc.

Date: 2014
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Citations: View citations in EconPapers (2)

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DOI: 10.1080/03610926.2012.673677

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