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Название: Statistics of Extremes Theory and Applications
Авторы: Jan Beirlant, Yuri Goegebeur, Jozef Teugels
Аннотация:
The key result obtained by Fisher and Tippett in 1928 on the possible limit laws
of the sample maximum has seemingly created the idea that extreme value theory
was something rather special, very different from classical central limit theory. In
fact, the number of publications dealing with statistical aspects of extremes dated
before 1970 is at most a dozen. The book by E. J. Gumbel, published by Columbia
University Press in 1958, has for a long time been considered as the main referential
work for applications of extreme value theory in engineering subjects. A close look
at this seminal publication shows that in the early stages one tried to approach
extreme value theory via central limit machinery. During the decade following
its appearance, no change occurred in the lack of interest among probabilists and
statisticians who contributed only a very limited number of relevant papers.
From the theoretical point of view, the 1970 doctoral dissertation by L. de
Haan On Regular Variation and its Applications to the Weak Convergence of Sample
Extremes seems to be the starting point for theoretical developments in extreme
value theory. For the first time, the probabilistic and stochastic properties of sample
extremes were developed into a coherent and attractive theory, comparable to the
theory of sums of random variables. The statistical aspects had to wait even longer
before they received the necessary attention.