Berry–Esseen bounds for typical weighted sums
نویسندگان
چکیده
منابع مشابه
Strong Laws for Weighted Sums of Negative Dependent Random Variables
In this paper, we discuss strong laws for weighted sums of pairwise negatively dependent random variables. The results on i.i.d case of Soo Hak Sung [9] are generalized and extended.
متن کاملstrong laws for weighted sums of negative dependent random variables
in this paper, we discuss strong laws for weighted sums of pairwise negatively dependent random variables. the results on i.i.d case of soo hak sung [9] are generalized and extended.
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where p is a prime power , χ mod p is a Dirichlet character, a, b, n are integers with n ≥ 2. The first sum was studied in connection with Waring’s problem and we have a classical result due to professor Hua [10]. The second sum has not been studied before as far as the authors know. We hope it can be used in the work of generalizing Waring’s problem. In [6], Davenport and Heilbronn showed that...
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Let {Xi} be a sequence of independent, identically distributed random variables with an intermediate regularly varying right tail F̄ . Let (N,C1, C2, . . .) be a nonnegative random vector independent of the {Xi} with N ∈ N ∪ {∞}. We study the weighted random sum SN = ∑Ni=1 CiXi , and its maximum, MN = sup1≤k<N+1 ∑ki=1 CiXi . This type of sum appears in the analysis of stochastic recursions, incl...
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The tail probabilities of two weighted sums of independent gamma random variables are compared when the first vector of weights majorizes the second vector of weights. The conjecture that the two cumulative distribution .functions cross exactly once is established in four special cases by means of the variation-diminishing property of totally positive kernels. Bounds are obtained for the locati...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2018
ISSN: 1083-6489
DOI: 10.1214/18-ejp195