Approximations to Distributions of Extremes
The nondegenerate limiting d.f.’s of sample maxima X n:n are the Frechet d.f.’s G1,α, Weibull d.f.’s G2,α, and the Gumbel d.f. G3. Thus, with regard to the variety of limiting d.f.’s the situation of the present chapter turns out to be more complex than that of the preceding chapter, where weak regularity conditions guarantee the asymptotic normality of the order statistics.
KeywordsOrder Statistic Weak Convergence Variational Distance Sample Maximum Hellinger Distance
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