1,721,006 research outputs found
On multivariate Gaussian tails
No full textMultivariate Mills ratio, Gaussian random sequences, tail asymptotics, quadratic programming,
Domination of sample maxima and related extremal dependence measures
No full textFor a given d-dimensional distribution function (df) H we introduce the class of dependence measures μ(H, Q) = −E{n H(Z1, . . . , Zd)}, where the random vector (Z1, . . . , Zd) has df Q which has the same marginal dfs as H. If both H and Q are max-stable dfs, we show that for a df F in the max-domain of attraction of H, this dependence measure explains the extremal dependence exhibited by F. Moreover, we prove that μ(H, Q) is the limit of the probability that the maxima of a random sample from F is marginally dominated by some random vector with df in the max-domain of attraction of Q. We show a similar result for the complete domination of the sample maxima which leads to another measure of dependence denoted by λ(Q, H). In the literature λ(H, H), with H a max-stable df, has been studied in the context of records, multiple maxima, concomitants of order statistics and concurrence probabilities. It turns out that both μ(H, Q) and λ(Q, H) are closely related. If H is max-stable we derive useful representations for both μ(H, Q) and λ(Q, H). Our applications include equivalent conditions for H to be a product df and F to have asymptotically independent components
A new family of bivariate max-infinitely divisible distributions
Get PDFExtremes of triangular arrays, Weibull max-domain of attraction, Max-infinitely divisible distribution, Weak convergence, Generalised symmetrised Dirichlet distributions, Asymptotically spherical random vectors,
Representations of max-stable processes via exponential tilting
No full textThe recent contribution Dieker & Mikosch (2015) [1] obtained important representations of max-stable stationary Brown-Resnick random fields ζZ with a spectral representation determined by a Gaussian process Z. With motivations from \cite{DM} we derive for some general Z, representations for ζZ via exponential tilting of Z. Our main findings concern a) Dieker-Mikosch representations of max-stable processes, b) two-sided extensions of stationary max-stable processes, c) inf-argmax representation of any max-stable distribution, and d) new formulas for generalised Pickands constants. Our applications include new conditions for the stationarity of ζZ, a characterisation of Gaussian random vectors and an alternative proof of Kabluchko's characterisation of Gaussian processes with stationary increments
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