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On inverse moments of nonnegative weakly convergent random variables. (Chinese. English summary) Zbl 1141.60309

Summary: The authors give sufficient conditions under which \(\lim\limits_{n \to \infty}(1+EX_n)^\alpha E\frac{1}{(1+X_n)^\alpha}=1\) for sequences of nonnegative weakly convergent random variables when their \((2+\delta)\)th moments are finite and \(\alpha >0\) . It generalizes the results of A. Kaluszka and A. Okolewski [Statist. Probab. Lett. 66, 45–50 (2004; Zbl 1116.60306)] and gives complete proofs for their Theorem \(3\) and Theorem \(4\).

MSC:

60E15 Inequalities; stochastic orderings
60F05 Central limit and other weak theorems

Citations:

Zbl 1116.60306
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