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...
متن کاملNon-uniform spacings processes
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,...
متن کاملLimit results for ordered uniform spacings
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.
متن کاملIncomplete Dirichlet Integrals with Applications to Ordered Uniform Spacings
Sob& Uppuluri, and Frankowski, (Selected Tables in Math. Statistics, Vol. IV. Amer. Math. Sot., Providence, R. I., 1977) consider an incomplete Dirichlet integral of type I with several interesting applications connected with the multinomial distribution and provide tables of this integral along with other useful tables. Two incomplete Dirichlet integrals are discussed here along with some usef...
متن کاملUpper and Lower Class Sequences for Minimal Uniform Spacings
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...
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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