Let X1,X2,... be independent bivariate claim sizes arising from an insurance portfolio. The number of claims occurring in the time interval [0,t] is denoted by N(t). We investigate in this paper distributional and asymptotic properties of the following point process:with XN(t):N(t), the...

Let {Xn, n[greater-or-equal, slanted]1} be a sequence of independent random variables with common continuous distribution function F and constants. In this short note an asymptotic evaluation of P{max1[less-than-or-equals, slant]i[less-than-or-equals, slant]n Xi[less-than-or-equals,...

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...

The paper deals with random vectors in , possessing the stochastic representation , where R is a positive random radius independent of the random vector and is a non-singular matrix. If is uniformly distributed on the unit sphere of , then for any integer m<d we have the stochastic representations and , with W>=0, such that W2 is a beta distributed...</d>

Let {Xn,n[greater-or-equal, slanted]1} be iid elliptical random vectors in and let I,J be two non-empty disjoint index sets. Denote by Xn,I,Xn,J the subvectors of Xn with indices in I,J, respectively. For any such that aJ is in the support of X1,J the conditional random sample Xn,IXn,J=aJ,n=1...

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...

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...