Abstract
For a given random sample from some underlying multivariate distribution F we consider the domination of the component-wise maxima by some independent random vector W with distribution function G. We show that the probability that certain components of the sample maxima are dominated by the corresponding components of W can be approximated under the assumptions that both F and G are in the max-domain of attraction of some max-stable distribution functions. We study further some basic probabilistic properties of the dominated components of sample maxima by W.
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