Sharp Probability Estimates for Generalized Smirnov Statistics
نویسنده
چکیده
We give sharp, uniform estimates for the probability that the empirical distribution function for n uniform-[0, 1] random variables stays to one side of a given line.
منابع مشابه
Generalized Smirnov Statistics and the Distribution of Prime Factors
(1.2) log2 pj ≤ αj + β (1 ≤ j ≤ ω(n)), where α ≥ 0 and log2 y denotes log log y. The distribution of integers satisfying (1.1) is important in the study of the distribution of divisors of integers (see [3]; Ch. 2 of [4]). We present here estimates for Nk(x;α, β) = #{n ≤ x : ω(n) = k, (1.1)}, Mk(x;α, β) = #{n ≤ x : ω(n) = k, (1.2)}. It is a relatively simple matter, at least heuristically, to re...
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