On the asymptotic approximation of inverse moment for non negative random variables
ABSTRACT In this paper, we have studied the asymptotic approximation of inverse moment. Let {Zn} be non negative random variables, where the truncated random variables satisfy the Rosenthal-type inequality. Denote . The inverse moment can be asymptotically approximated by , and the growth rate is presented as . Meanwhile, we obtain a result for a function f(x) satisfying certain conditions. On the other hand, if , then the growth rate is presented as |E(a + Xn)− α/(a + EXn)− α − 1| = O(1/EXn). Our results generalize and improve some corresponding ones. Finally, some examples of inverse moment are illustrated.