Upper and Lower Class Sequences for Minimal Uniform Spacings
نویسنده
چکیده
In this paper we investigate the asymptotic behavior of the k-th smallest uniform spacing. Among other things, a complete characterization of upper and lower class sequences is obtained. The asymptotic behavior is similar in many respects to that of the minimum of independent uniformly distributed random variables. Let X1 , . . . ,X , be independent identically distributed uniform (0, 1) random variables with order statistics 0 < X 1 (n) < . . . < X,(n) < 1, and let u, be any sequence of positive numbers. Geffroy (1958/1959) has shown that if u,/n~., then 0 P(nXl(n)<u . i.o.) = when u, < oo = o 0
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