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Penultimate approximation for the excesses

Abstract : Let F be a distribution function (d.f.) in the maximum domain of attraction of an extreme value distribution H-gamma; then, F-u, d.f. of the excesses over u, converges, when u tends to s(+)(F), the end-point of F. to G(gamma,sigma (u)) (x), the d.f. of the Generalized Pareto Distribution. We provide conditions that ensure, for gamma > -1, the existence of a function Lambda satisfying lim(u-->s+(F))Lambda (u) = gamma such that [GRAPHICS] converges to 0 faster than [GRAPHICS] (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.
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Rym Worms. Penultimate approximation for the excesses. Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2001, 332 (11), pp.1025--1030. ⟨10.1016/S0764-4442(01)01980-2⟩. ⟨hal-00693729⟩



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