Penultimate approximation for the distribution of the excesses
ESAIM: Probability and Statistics, Tome 6 (2002), pp. 21-31.

Let F be a distribution function (d.f) in the domain of attraction of an extreme value distribution H γ ; it is well-known that F u (x), where F u is the d.f of the excesses over u, converges, when u tends to s + (F), the end-point of F, to G γ (x σ(u)), where G γ is the d.f. of the Generalized Pareto Distribution. We provide conditions that ensure that there exists, for γ>-1, a function Λ which verifies lim us + (F) Λ(u)=γ and is such that Δ(u)=sup x[0,s + (F)-u[ |F ¯ u (x)-G ¯ Λ(u) (x/σ(u))| converges to 0 faster than d(u)=sup x[0,s + (F)-u[ |F ¯ u (x)-G ¯ γ (x/σ(u))|.

DOI : 10.1051/ps:2002002
Classification : 60G70, 62G20
Mots clés : generalized Pareto distribution, excesses, penultimate approximation, rate of convergence
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Worms, Rym. Penultimate approximation for the distribution of the excesses. ESAIM: Probability and Statistics, Tome 6 (2002), pp. 21-31. doi : 10.1051/ps:2002002. http://www.numdam.org/articles/10.1051/ps:2002002/

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