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Contents of PMS, Vol. 31, Fasc. 2,
pages 331 - 347
 

KIEFER’S LAW OF THE ITERATED LOGARITHM FOR THE VECTOR OF UPPER ORDER STATISTICS

Rasbagh Vasudeva
Alireza Yousefi Moridani

Abstract: Let (X ) n be a sequence of independent identically distributed random variables with a common continuous distribution function and let M j,n denote the j th upper order statistic among X ,X ,...,X 1 2 n , n ≥ j . For a large class of distributions, we obtain the law of the iterated logarithm for (M ,M ) 1,n 2,n , properly normalized. As a consequence, we establish a law of the iterated logarithm for the spacings (M - M ) 1,n 2,n .

2000 AMS Mathematics Subject Classification: Primary: 60F15.

Keywords and phrases: Law of the iterated logarithm, upper order statistics, regularly varying function.

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