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 + EXn}(-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)}.
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