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Strong laws for ratios of order statistics from exponentials

Vol. 10 No. 1 (2015) P.101~P.111

ABSTRACT

The random variables examined are independent and identically distributed expo- nentials. The mean of these random variables can change from sample to sample. Within each sample we observe the ratio of various order statistics. Then we establish strong laws for these ratios. The most important statistic is the ratio of the two smallest order statistics within each sample. The distribution of this statistic is very interesting. It has infinite mean, but barely, which produces a very unusual strong law.

KEYWORDS
almost sure convergence, order statistics, regular variation, strong laws of large numbers

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 60F15

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