The <Emphasis FontCategory="NonProportional">RngStreams software package provides one viable solution to the problem of creating independent random number streams for simulations in parallel processing environments. Techniques are presented for effectively using <Emphasis FontCategory="NonProportional">RngStreams with <Emphasis FontCategory="NonProportional">C++ programs that are parallelized via <Emphasis FontCategory="NonProportional">OpenMP or <Emphasis FontCategory="NonProportional">MPI. Ways...</emphasis></emphasis></emphasis></emphasis></emphasis>

We give a necessary and sufficient condition for a d-dimensional Lévy process to be in the matrix normalized domain of attraction of a d-dimensional normal random vector, as t↓0. This transfers to the Lévy case classical results of Feller, Khinchin, Lévy and Hahn and Klass for random walks....

Let (Ut,Vt) be a bivariate Lévy process, where Vt is a subordinator and Ut is a Lévy process formed by randomly weighting each jump of Vt by an independent random variable Xt having cdf F. We investigate the asymptotic distribution of the self-normalized Lévy process Ut/Vt at 0 and at ∞. We...

Let X1,n[less-than-or-equals, slant]...[less-than-or-equals, slant]Xn,n be the order statistics of n independent random variables with a common distribution function F and let kn be positive numbers such that kn -- [infinity] and . With suitable centering and norming, we investigate the weak...

Stute (1982) and Mason, Shorack and Wellner (1983) have recently completed a thorough study of the limiting behavior of the oscillation of the uniform empirical process. In this paper, the corresponding oscillation behavior of the uniform empirical quantile process is investigated. It is shown...

The estimated weighted empirical quantile process is introduced, and under mild regularity conditions is shown to converge weakly in L2(0, 1) to a Gaussian process. This leads to an elementary approach to the derivation of the asymptotic null distribution of Cramér-von Mises type statistics for...

One and two sample rank statistics are shown in general to be more efficient in the Bahadur sense than their sequential rank statistic analogues as defined by Mason (1981, Ann. Statist.9 424-436) and Lombard (1981, South African Statist. J.15 129-152), even though the two families of statistics...

Strong limit theorems are obtained for maximal and minimal multivariate kn-spacings, where {kn}n=1[infinity] is a sequence of positive integers satisfying kn = 0(log n). The shapes, in terms of which these spacings are defined, are allowed to be quite general. They must only satisfy certain...

Let [alpha]n and un be the uniform empirical and quantile processes. We investigate the asymptotic distribution of the suprema of [alpha]n(s)/(s(1 - s))1/2±[nu] and un(s)/(s(1 - s))1/2±[nu] with , when the supremum is taken over ranges, depending on n, in the middle of the interval [0, 1],...