Penultimate approximation for the distribution of the excesses
ESAIM: Probability and Statistics, Volume 6  (2002), p. 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 : https://doi.org/10.1051/ps:2002002
Classification:  60G70,  62G20
Keywords: generalized Pareto distribution, excesses, penultimate approximation, rate of convergence
@article{PS_2002__6__21_0,
     author = {Worms, Rym},
     title = {Penultimate approximation for the distribution of the excesses},
     journal = {ESAIM: Probability and Statistics},
     publisher = {EDP-Sciences},
     volume = {6},
     year = {2002},
     pages = {21-31},
     doi = {10.1051/ps:2002002},
     zbl = {0992.60056},
     mrnumber = {1888136},
     language = {en},
     url = {http://www.numdam.org/item/PS_2002__6__21_0}
}
Worms, Rym. Penultimate approximation for the distribution of the excesses. ESAIM: Probability and Statistics, Volume 6 (2002) , pp. 21-31. doi : 10.1051/ps:2002002. http://www.numdam.org/item/PS_2002__6__21_0/

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