A note on sums and maxima of independent, identically distributed random variables
نویسندگان
چکیده
منابع مشابه
Comparison of Sums of Independent Identically Distributed Random Variables
Let Sk be the k-th partial sum of Banach space valued independent identically distributed random variables. In this paper, we compare the tail distribution of ‖Sk‖ with that of ‖Sj‖, and deduce some tail distribution maximal inequalities. The main result of this paper was inspired by the inequality from [dP–M] that says that Pr(‖X1‖ > t) ≤ 5 Pr(‖X1 +X2‖ > t/2) whenever X1 and X2 are independent...
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متن کاملA Note on Sums of Independent Random Variables
provided (Xn) are either symmetric or positive, and in the first case p ≥ 2, and in the second case p ≥ 1. The main novelty here is the fact that, contrary to the classical inequalities, the constants here are independent of p. Certain particular cases of Lata la’s result had been known earlier (see e.g. Hitczenko (1993), Gluskin and Kwapień (1995) or Hitczenko, Montgomery-Smith and Oleszkiewic...
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Frequently the need arises for the computer generation of variates that are exact/y distributed as 2 = max(X,, . , X.) where X,, . . . , X, form a sequence of independent identically distributed random variables. For large n the individual generation of the Xi’s is unfeasible, and the inversion-of-a-beta-variate is potentially inaccurate. In this paper, we discuss and compare the corrected inve...
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Abstract. Let X1, X2, . . . be a sequence of independent and identically distributed random variables, and put Sn = X1 + · · ·+ Xn. Under some conditions on the positive sequence τn and the positive increasing sequence an, we give necessary and sufficient conditions for the convergence of ∑ ∞ n=1 τnP (|Sn| ≥ εan) for all ε > 0, generalizing Baum and Katz’s (1965) generalization of the Hsu-Robbi...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1984
ISSN: 0386-2194
DOI: 10.3792/pjaa.60.353