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Rate of convergence for the generalized Pareto approximation of the excesses

Abstract : Let F be a distribution function in the domain of attraction of an extreme-value distribution H-.gamma If F-u is the distribution function of the excesses over u and G(gamma) the distribution function of the generalized Pareto distribution, then it is well known that F-u(x) converges to G(gamma)(x/sigma(u)) as u tends to the end point of F, where sigma is an appropriate normalizing function. We study the rate of (uniform) convergence to 0 of (F) over bar (u)(x) - (G) over bar (gamma)((x + u - alpha(u))/sigma(u)), where alpha and sigma are two appropriate normalizing functions.
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Submitted on : Wednesday, May 2, 2012 - 4:58:54 PM
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Jean-Pierre Raoult, R Worms. Rate of convergence for the generalized Pareto approximation of the excesses. Advances in Applied Probability, Applied Probability Trust, 2003, 35 (4), pp.1007--1027. ⟨10.1239/aap/1067436332⟩. ⟨hal-00693464⟩

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