Convergence rates for the ultimate and pentultimate approximations in extreme-value theory

DOI10.2307/1427026zbMath0496.62019OpenAlexW2314729957MaRDI QIDQ3959945

Jonathan P. Cohen

Publication date: 1982

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/1427026

zbMATH Keywords

domain of attractionpenultimate approximationuniform rates of convergenceextreme-value distribution

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Order statistics; empirical distribution functions (62G30)

Related Items (18)

Penultimate versus ultimate in statistical theory of extremes. A simulation study ⋮ Rates of uniform convergence of extreme order statistics ⋮ Penultimate approximation for the distribution of the excesses ⋮ Unnamed Item ⋮ Approximation of the distribution of excesses through a generalized probability-weighted moments method ⋮ Complete asymptotic expansions for normal extremes ⋮ Asymptotic behavior of the extrapolation error associated with the estimation of extreme quantiles ⋮ A comparison of estimators of functionals of the distribution of a maximum ⋮ EVT-based estimation of risk capital and convergence of high quantiles ⋮ Bayesian inference for extremes: accounting for the three extremal types ⋮ Convergence Rate of Extremes for the General Error Distribution ⋮ Asymptotic behaviour of the probability-weighted moments and penultimate approximation ⋮ Rate of convergence for the generalized Pareto approximation of the excesses ⋮ Convergence of distributions of extremal independent random variables ⋮ The maximum size of the planar sections of random spheres and its application to metallurgy ⋮ Rates of convergence of \(\alpha\)-stable random motions ⋮ Scaling of High-Quantile Estimators ⋮ Unnamed Item

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