Glivenko-Cantelli-type theorems for weighted empirical distribution functions based on uniform spacings

Let U1, U2,… be a sequence of independent r.v.'s having the uniform distribution on (0, 1). Let n be the empirical distribution based on the transformed uniform spacings Di,nG(nDi,n), i = 1, 2,…, n, where G is the exp(1) d.f. and Di,n is the ith spacing based on U1, U2,…,Un-1. The main purpose of this paper is the study of the almost sure behaviour of lim supn ¿ 8 ¿n,a(q, ) and lim supn¿8 ¿n,r(q, ), where ¿n,a(q, ) = sup0 0 and certain weight functions q and . Moreover, the weak behaviour of the statistics will be examined briefly. It turns out that compared with the uniform empirical process (i.i.d. case) the considered weighted Kolmogorov—Smirnov- and Cramér—von Mises-type statistics behave differently in the right tail only as far as almost sure convergence is concerned. There is no difference in the weak sense. The results can be applied to the study of linear combinations of functions of ordered spacings

On the approximation of an integral by a sum of random variables

We approximate the integral of a smooth function on [0,1], where values are only known at n random points (i.e., a random sample from the uniform-(0,1) distribution), and at 0 and 1. Our approximations are based on the trapezoidal rule and Simpson's rule (generalized to the non-equidistant case), respectively. In the first case, we obtain an n2-rate of convergence with a degenerate limiting distribution; in the second case, the rate of con-vergence is as fast as n3½, whereas the limiting distribution is Gaussian then

Flecs, a flexible coupling shell - Parallel application to fluid-structure interaction

In this paper we discuss the second version of FLECS, a generic, open-source coupling shell that can be used to join two or more arbitrary solvers. In general multidisciplinary computations are very computing-intensive. A remedy against long computing times is large-scale parallelism. The challenge of the present parallelization work is to obtain acceptable computing times and to get rid of severe memory requirements that exist on sequential machines, for the generic flow problems at hand. The aim is to provide a flexible platform for developing new data transfer algorithms and coupling schemes

FLECS, a Flexible Coupling Shell Parallel Application to Fluid-Structure Interaction

In this paper we discuss the second version of FLECS, a generic, open-source coupling shell that can be used to join two or more arbitrary solvers. In general multidisciplinary computations are very computing-intensive. A remedy against long computing times is large-scale parallelism. The challenge of the present parallelization work is to obtain acceptable computing times and to get rid of severe memory requirements that exist on sequential machines, for the generic flow problems at hand. The aim is to provide a flexible platform for developing new data transfer algorithms and coupling schemes