With the df F of the rv X we associate the natural exponential family of df's F[lambda] wheredF[lambda](x)=e[lambda]x dF(x)/Ee[lambda]Xfor . Assume [lambda][infinity]=sup [Lambda][less-than-or-equals, slant][infinity] does not lie in [Lambda]. Let [lambda][short up arrow][lambda][infinity], then...

Suppose {Xnn[greater-or-equal, slanted]-0} are random variables such that for normalizing constants an0, bn, n[greater-or-equal, slanted]0 we have Yn(·)=(X[n, ·]-bn/an = Y(·) in D(0.[infinity]) . Then an and bn must in specific ways and the process Y possesses a scaling property. If...

{Xn,n[greater-or-equal, slanted]1} are i.i.d. random variables with continuous d.f. F(x). Xj is a record value of this sequence if Xjmax{X1,...,Xj-1}. Consider the sequence of such record values {XLn,n[greater-or-equal, slanted]1}. Set R(x)=-log(1-F(x)). There exist Bn 0 such that XLn/Bn--1. in...

We consider stationary autoregressive processes of order p which have positive innovations. We propose consistent parameter estimators based on linear programming. Under conditions, including regular variation of either the left or right tail of the innovations distribution, we prove that the...

We consider limit distributions of extremes of a process {Yn} satisfying the stochastic difference equation Yn-AnYn-1+Bn, n[greater-or-equal, slanted]1,Y0[greater-or-equal, slanted]0, where {An, Bn} are i.i.d. 2+-valued random pairs, A special case of interest is when {Yn} is derived from a...

We present a formulation of subexponential and exponential tail behavior for multivariate distributions. The definitions are necessarily in terms of vague convergence of Radon measures rather than of ratios of distribution tails. With the proper setting, we show that if all one dimensional...

(Xn)n=1,2,... is a sequence of independent, identically distributed random vectors in 2. Say Xn is a record if there is a record simultaneously in both coordinates at index n. The total number of records of a sequence is frequently finite so we consider the behaviour of the records in a fixed...