Almost sure convergence of the distributional limit theorem for order statistics

• Autorzy: Peng L. , Qi Y.
• Języki publikacji: EN

Abstrakty

EN

Let X_n, n ≥ 1, be a sequence of independent and identically distributed random variables and X_n,1 ≤ X_n,2 ≤...≤ X_n,n denote the order statistics of X₁,…, X_n. For any sequence of integers {k_n} with 1 ≤ k_n ≤ n and lim_n→∞min {k_n, n − k_n + 1} = ∞, if there exist constants a_n > 0, b_n ∈ R and some non-degenerate distribution function G such that (X_n,kn − b_n)/ a_n converges in distribution to G, then with probability one [wzór] = G(x) for all x ∈ C (G), where C (G) is the set of continuity points of G.

Słowa kluczowe

EN

almost sure convergence; distributional limit theorem; order statistics

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2003
• Tom: Vol. 23, Fasc. 2
• Strony: 217--228
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Peng L.

• School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, U.S.A.

autor

Qi Y.

• Department of Mathematics and Statistics, University of Minnesota Duluth, Campus Center 140, 1117 University Drive, Duluth, MN 55812, U.S.A.

Bibliografia

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