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Let $F$ be a distribution function (d.f) in the domain of attraction of an extreme value distribution $H_{\gamma }$; it is well-known that $F_u\left(x\right)$, where $F_u$ is the d.f of the excesses over $u$, converges, when $u$ tends to $s_{+}\left(F\right)$, the end-point of $F$, to $G_{\gamma }\left(\frac{x}{\sigma \left(u\right)}\right)$, where $G_{\gamma }$ is the d.f. of the Generalized Pareto Distribution. We provide conditions that ensure that there exists, for $\gamma \>-1$, a function $\Lambda$ which verifies ${lim}_{u\to s_{+}\left(F\right)}\Lambda \left(u\right)=\gamma$ and is such that $\Delta \left(u\right)={sup}_{x\in [0,s_{+}\left(F\right)-u[}|{\overline{F}}_u\left(x\right)-{\overline{G}}_{\Lambda \left(u\right)}(x/\sigma \left(u\right))|$ converges to $0$ faster than $d\left(u\right)={sup}_{x\in [0,s_{+}\left(F\right)-u[}|{\overline{F}}_u\left(x\right)-{\overline{G}}_{\gamma }(x/\sigma \left(u\right))|$.

Let be a distribution function (d.f) in the domain of attraction of an extreme value distribution $H_{\gamma }$; it is well-known that , where is the d.f of the excesses over , converges, when tends to , the end-point of , to $G_{\gamma }\left(\frac{x}{\sigma \left(u\right)}\right)$, where $G_{\gamma }$ is the d.f. of the Generalized Pareto Distribution. We provide conditions that ensure that there exists, for $\gamma >-1$, a function which verifies ${lim}_{u\to s_{+}\left(F\right)}\Lambda \left(u\right)=\gamma$ and is such that $\Delta \left(u\right)={sup}_{x\in [0,s_{+}\left(F\right)-u[}|{\overline{F}}_u\left(x\right)-{\overline{G}}_{\Lambda \left(u\right)}(x/\sigma \left(u\right))|$ converges to faster than $d\left(u\right)={sup}_{x\in [0,s_{+}\left(F\right)-u[}|{\overline{F}}_u\left(x\right)-{\overline{G}}_{\gamma }(x/\sigma \left(u\right))|$.

The P.O.T. method (Peaks Over Threshold) consists in using the generalized Pareto distribution (GPD) as an approximation for the distribution of excesses over a high threshold. In this work, we use a refinement of this approximation in order to estimate second order parameters of the model using the method of probability-weighted moments (PWM): in particular, this leads to the introduction of a new estimator for the second order parameter , which will be compared to other recent estimators through...

The P.O.T. method (Peaks Over Threshold) consists in using the generalized Pareto distribution (GPD) as an approximation for the distribution of excesses over a high threshold. In this work, we use a refinement of this approximation in order to estimate second order parameters of the model using the method of probability-weighted moments (PWM): in particular, this leads to the introduction of a new estimator for the second order parameter , which will be compared to other recent estimators through...

The P.O.T. (Peaks-Over-Threshold) approach consists of using the Generalized Pareto Distribution (GPD) to approximate the distribution of excesses over a threshold. We use the probability-weighted moments to estimate the parameters of the approximating distribution. We study the asymptotic behaviour of these estimators (in particular their asymptotic bias) and also the functional bias of the GPD as an estimate of the distribution function of the excesses. We adapt penultimate approximation results...

The P.O.T. (Peaks-Over-Threshold) approach consists of using the Generalized Pareto Distribution (GPD) to approximate the distribution of excesses over a threshold. We use the probability-weighted moments to estimate the parameters of the approximating distribution. We study the asymptotic behaviour of these estimators (in particular their asymptotic bias) and also the functional bias of the GPD as an estimate of the distribution function of the excesses. We adapt penultimate approximation results...