منابع مشابه
Non-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 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...
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 کاملExact Laws for Sums of Logarithms of Uniform Spacings
Abstract: In this paper we provide some simple expressions for the exact law of sums of logarithms of uniform spacings. We also obtain closed form expressions for the corresponding cumulants of arbitrary order, in terms of the Riemann zeta function. Our results follow from two representations of this statistic through sums of independent random variables, the latter being of independent interes...
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...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 1987
ISSN: 0304-4149
DOI: 10.1016/0304-4149(87)90190-6