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Let Nn = {1, 2,. .. , n}. Elements are drawn from the set Nn with replacement, assuming that each element has probability 1/n of being drawn. We determine the limiting distributions for the waiting time until the given portion of pairs jj, j ∈ Nn, is sampled. Exact distributions of some related random variables and their characteristics are also obtained.

Let (Xn) be a strictly stationary sequence with a marginal distribution function F such that 1 − F (x) = x −α L(x), x > 0, where α > 0 and L(x) is a slowly varying function. We assume that only observations of (X n) are available at certain points. Under assumption of weak dependency we proved the consistency of Hill's estimator of the tail index α based on… (More)

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