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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 22, Fasc. 2,
pages 211 - 220
 

LIMIT THEOREMS FOR ARRAYS OF MAXIMAL ORDER STATISTICS

André Adler

Abstract: Let (X,X ,1 < j < m ,n > 1) nj n be independent and identically distributed random variables with the Pareto distribution. Let X n(k) be the k -th largest order statistic from the n -th row of our array. This paper establishes unusual limit theorems involving weighted sums for the sequence (X ,n > 1). n(k)

2000 AMS Mathematics Subject Classification: 60F0S, 60F1S.

Key words and phrases: Almost sure convergence; weak law of large numbers; generalized law of the iterated logarithm.

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