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Approximations to Distributions of Extremes

  • R.-D. Reiss
Part of the Springer Series in Statistics book series (SSS)

Abstract

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.

Keywords

Order Statistic Weak Convergence Variational Distance Sample Maximum Hellinger Distance 
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Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • R.-D. Reiss
    • 1
  1. 1.Fachbereich 6, MathematikUniversität Gesamthochschule SiegenSiegenFederal Republic of Germany

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