Open AccessStrong laws for the largest ratio of adjacent order statistics
Author(s) -
André Adler
Publication year - 2017
Publication title -
bulletin of the institute of mathematics academia sinica new series
Language(s) - English
Resource type - Journals
eISSN - 2304-7909
pISSN - 2304-7895
DOI - 10.21915/bimas.2017402
Subject(s) - statistics , order statistic , order (exchange) , law , mathematics , political science , economics , finance
Consider independent and identically distributed random variables {Xn,k, 1 ≤ k ≤ mn, n ≥ 1}. We order this data set, Xn(1) < Xn(2) < Xn(3) < · · · < Xn(mn−1) < Xn(mn). Then we find the ratio of these adjacent order statistics. Our random variable of interest is the largest of these adjacent ratios, max2≤k≤mn Xn(k)/Xn(k−1). We obtain various limit theorems for this random variable.
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