Limit theorems for arrays of maximal order statistics

• Autorzy: Adler A.
• Języki publikacji: EN

Abstrakty

EN

Let {X, X_nj,1≤j≤m_n, n≥1} be independent and identically distributed random variables with the Pareto distribution. Let X_n(k) be the k-th largestorder statistic from then-th row of our array. This paper establishes unusual limit theorems involving weighted sums for the sequence {X_n(k), n≥1}.

Słowa kluczowe

EN

almost sure convergence; weak law of large numbers; generalized law; iterated logarithm

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2002
• Tom: Vol. 22, Fasc. 2
• Strony: 211--220
• Opis fizyczny: Biblogr. 4 poz.

Twórcy

autor

Adler A.

• Department of Mathematics Illinois Institute of Technology Chicago, Illinois, 60616

Bibliografia

• [1] A. Adler, Generalized one-sided laws of the iterated logarithm for random variables barely with or without finite mean, J. Theoret. Probab. 3 (1990), pp. 587-598.
• [2] Y. S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales, 3-rd ed., Springer, New York 1997.
• [3] I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, 4-th ed., Academic Press, New York 1980.
• [4] M. Klass and H. Teicher, Iterated logarithm laws for asymmetric random variables barely with or without finite mean, Ann. Probab. 5 (1977), pp. 861-874.