Expansions for Quantiles and Multivariate Moments of Extremes for Heavy Tailed Distributions
Keywords:Bell polynomials, extremes, inversion theorem, moments, quantiles
(...)The study of the asymptotes of the moments of Xn,r has been of considerable interest. McCord  gave a first approximation to the moments of Xn,1 for three classes. This showed that a moment of Xn,1 can behave like any positive power of n or n1 = log n. (Here, log is to the base e.) Pickands  explored the conditions under which various moments of (Xn,1 − bn) /an converge to the corresponding moments of the extreme value distribution. It was proved that this is indeed true for all F in the domain of attraction of an extreme value distribution provided that the moments are finite for sufficiently large n. Nair  investigated the limiting behavior of the distribution and the moments of Xn,1 for large n when F is the standard normal distribution function. (...)
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