On Fatou-type lemma for monotone moments of weakly convergent random variables. (English) Zbl 1116.60308

Summary: Sufficient conditions for convergence of monotone moments of weakly convergent random variables, concerning the rate of convergence, are given. They are often more convenient than the necessary and sufficient uniform integrability condition. Some asymptotic evaluations for inverse moments are presented.


60E05 Probability distributions: general theory
62E20 Asymptotic distribution theory in statistics
Full Text: DOI


[1] Christoph, G., Werner, W., 1992. Convergence theorems with a stable limit law. In: Mathematical Research, Vol. 70. Akademie-Verlag, Berlin. · Zbl 0773.60012
[2] Fujioka, T., Asymptotic approximations of the inverse moments of the noncentral chi-squared variable, J. Japan statist. soc., 31, 99-109, (2001) · Zbl 1031.62011
[3] Garcia, N.L.; Palacios, J.L., On inverse moments of nonnegative random variables, Statist. probab. lett., 53, 235-239, (2001) · Zbl 0991.60003
[4] Helmers, R., 1982. Edgeworth expansions for linear combinations of order statistics. In: Mathematical Centre Tract, Vol. 105. Math. Centrum, Amsterdam. · Zbl 0485.62017
[5] Jurlewicz, A.; Weron, K., Relaxation of dynamically correlated clusters, J. non-crystalline solids, 305, 112-121, (2002)
[6] Kallenberg, O., Foundations of modern probability, (2001), Springer New York
[7] Marciniak, E.; Wesołowski, J., Asymptotic Eulerian expansions for binomial and negative binomial reciprocals, Proc. amer. math. soc., 127, 3329-3338, (1999) · Zbl 0930.60004
[8] Petrov, V.V., Generalization of cramér’s limit theorem, Uspehi mat. nauk, 9, 195-202, (1954)
[9] Petrov, V.V., 1995. Limit theorems of probability theory. In: Sequences of Independent Random Variables. Clarendon Press, Oxford. · Zbl 0826.60001
[10] Pollard, D., 2001. Distance between multinomial and multivariate normal models [http://www.stat.yale.edu/polard].
[11] Ramsay, C.M., A note on random survivorship group benefits, ASTIN bull., 23, 149-156, (1993)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.