M. Isaev, I. Rodionov, Ruizhe Zhang, M. Zhukovskii
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引用次数: 2
Abstract
The central result of extreme value theory proved by Gnedenko [1] classifies all types of asymptotic distributions that the normalized maximum of a sample of independent identically distributed random variables could possibly have. Does a similar result hold if the variables are not identically distributed or are dependent? We consider a sequence of random vectors Xn = (X1,n, . . . , Xd,n) ∈ R, where d = d(n) ∈ N and n ∈ N. Let [d] := {1, . . . , d}. If, for any fixed x ∈ R, ∣∣∣∣P(max i∈[d] Xi,n ⩽ x)− ∏ i∈[d] P(Xi,n ⩽ x) ∣∣∣∣ → 0, as n →∞, (1)
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
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