The Asymptotic Theory of Extreme Order Statistics
Discusses the stochastic regularity in extreme behavior, presenting the asymptotic theory of extremes as the number of components making up the extremes increases indefinitely. Determines all limiting distributions under different sets of conditions and fully covering the multivariate extreme value theory. Offers for the first time in book form discussions of multivariate extreme value distributions (with full details), extreme value theory for dependent samples, and the almost sure behavior of extremes, extremes for random sample sizes, records and record times, and inequalities of estimates in the univariate case. Mathematically rigorous yet easily accessible, it is equally suitable for textbook adoption or as a major reference source.
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WEAK CONVERGENCE FOR INDEPENDENT AND IDENTICALLY
WEAK CONVERGENCE OF EXTREMES IN THE GENERAL CASE
DEGENERATE LIMIT LAWS ALMOST SURE RESULTS
6 other sections not shown
actual addition appeal apply arbitrary assume assumption asymptotic basic becomes bounds Chapter choice choose completes components conclusion Consequently consider constants continuous converges converges weakly Corollary defined definition dependent determine distribution function distribution function F(x domain of attraction equal equivalent established estimate evidently Example exchangeable Exercise exists exponential expressed extended extremes fact finite fixed formula Furthermore give given hand side Hence holds identically immediately implies increasing independent inequality integer interest leads Lemma Let X1 limiting distribution marginals mathematical maximum method nondegenerate normal notations Notice observations obtained particular points positive possible present probability problem proof prove random variables real numbers record relation Remark respectively satisfies sequence specific statement statistics sums tends Theorem theory tion turn unit variates vector yields zero