A Note on Reliability Properties of K-Record Statistics.
A note on the distributions of the maximum of linear Bernoulli processes.
Almost sure convergence for the maximum and the sum of nonstationary Gaussian sequences. (Almost sure convergence for the maximum and the sum of nonstationary guassian sequences.)
An almost sure limit theorem for the maxima of strongly dependent Gaussian sequences.
An extreme Markovian-evolutionary (EME) sequence.
The most general sequence, with Gumbel margins, generated by maxima procedures in an auto-regressive way (one step) is defined constructively and its properties obtained; some remarks for statistical estimation are presented.
Approximations et majorations optimales des statistiques d'ordre d'un échantillon
Asymptotic behaviour of the probability-weighted moments and penultimate approximation
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...
Asymptotic behaviour of the probability-weighted moments and penultimate approximation
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...