Maximal divergent uniform spacings
نویسندگان
چکیده
منابع مشابه
A Log Log Law for Maximal Uniform Spacings
McGill University Let X1 , X2, • . . be a sequence of independent uniformly distributed random variables on [0, 1] and Kn be the kth largest spacing induced by X 1 , X12 . We show that P(Kn < (log n log3n log 2)/n i .o .) = 1 where log, is the j times iterated logarithm. This settles a question left open in Devroye (1981) . Thus, we have lim inf(nKn log n + log3n) _ -log 2 almost surely, and li...
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We provide a joint strong approximation of the uniform spacings empirical pro1 cess and of the uniform quantile process by sequences of independent Gaussian processes. 2 This allows us to obtain an explicit description of the limiting Gaussian process generated by 3 the sample spacings from a non-uniform distribution. It is of the form B(t)+ (1− σF ){(1− 4 t) log(1 − t)} ∫ 1 0 {B(s)/(1 − s)}ds,...
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Let k:n = Xk,n − Xk−1,n(k = 1, 2, . . . , n+1) be the spacings based on uniform order statistics, provided X0,n = 0 and Xn+1,n = 1. Obtained from uniform spacings, ordered uniform spacings 0 = 0,n < 1,n < · · · < n+1,n , are discussed in the present paper. Distributional and limit results for them are in the focus of our attention.
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 1989
ISSN: 0304-4149
DOI: 10.1016/0304-4149(89)90074-4