Asymptotic approximation of inverse moments of nonnegative random variables

作者：Wu Tiee Jian^*; Shi Xiaoping; Miao Baiqi

来源：Statistics & Probability Letters, 2009, 79(11): 1366-1371.

DOI：10.1016/j.spl.2009.02.010

Let {Z(n). n >= 1} be a sequence of independent nonnegative r.v.'s (random variables) with finite second moments. it is shown that under a Lindeberg-type condition, the alpha th inverse moment E{a+X(n)}(-alpha) can be asymptotically approximated by the inverse of the alpha th moment {a + EX(n)}(-alpha) where a > 0, alpha > 0, and {X(n)} are the naturally-scaled partial Sums. Furthermore, it is shown that, when {Z(n)} only possess finite rth moments, 1 <= r < 2, the preceding asymptotic approximation can still be valid by using different norming constants which are the standard deviations of partial sums of suitably truncated {Z(n)}.

• 出版日期2009-6-1
• 单位中国科学技术大学