We show a lower bound for the boundary crossing probability P{[there exists]z[set membership, variant][0,1]:h(z)+B0(z)u(z)} with B0 a Brownian bridge, h a trend function and u a boundary function. By that we get also a lower bound for the boundary crossing probability P{[there exists]z[set...

Let {Xi, i[greater-or-equal, slanted]1} be a sequence of m-dependent stationary standard Gaussian random variables and some positive constants. In this note we generalise results of Raab (Extremes 1(3) (1999) 29.), who considered compound Poisson approximation for Wn=[summation...

Let {Xn, n[greater-or-equal, slanted]1} be a centered FGM random sequence and put . Motivated by the dependence structure of FGM distributions (see, e.g. Johnson and Kotz, Comm. Statist. 4 (1977) 415) we derive almost sure and max-limit almost sure convergence for and Mn, respectively.

Let , be a triangular array of independent elliptical random vectors in . In this paper we investigate the asymptotic behaviour of the multivariate maxima of this triangular array. Generalising previous results for the bivariate set-up, we show that the normalised maxima of this elliptical...

Let be a triangular array of independent bivariate elliptical random vectors. Hüsler and Reiss (1989. Statist. Probab. Lett. 7, 283-286) show that for the particular case that the array is Gaussian, the maxima of this array is in the max-domain of attraction of Hüsler-Reiss distribution...

Given a Brownian bridge B0 with trend g:[0,1]--[0,[infinity]), Y(z)=g(z)+B0(z),z[set membership, variant][0,1],we are interested in testing H0:g[reverse not equivalent]0 against the alternative K:g0. For this test problem we study weighted Kolmogorov testswhere c0 is a suitable constant and...

In this paper we consider bivariate triangular arrays given in terms of linear transformations of asymptotically spherical bivariate random vectors. We show under certain restrictions that the componentwise maxima of such arrays is attracted by a bivariate max-stable distribution function with...

Let be a Kotz Type III elliptical random vector in , and let tn,n=1 be positive constants such that limn--[infinity]tn=[infinity]. In this article we obtain an asymptotic expansion of . As an application we derive an approximation for the conditional excess distribution and show the asymptotic...

Let {Xn,n[greater-or-equal, slanted]1} be a sequence of independent random vectors in , with common continuous distribution function F. For fixed n[greater-or-equal, slanted]2, we say that a multiple maximum occurs among the sample points X1,...,Xn if Mn=Xi for some i=1,...,n, with Mn the...

Let (X,Y) be a bivariate elliptical random vector with associated random radius in the Gumbel max-domain of attraction. In this paper we obtain a second order asymptotic expansion of the joint survival probability and the conditional probability , for x,y large.