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Research Interests: Mathematics and Skew
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Research Interests: Philosophy and Humanities
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In various manufacturing industries it is important to investigate the presence of some chemical or harmful substances in lots of raw material or final products, in order to evaluate if they are in conformity to requirements. In this work... more
In various manufacturing industries it is important to investigate the presence of some chemical or harmful substances in lots of raw material or final products, in order to evaluate if they are in conformity to requirements. In this work we highlight the adequacy of the inflated Pareto distribution to model measurements obtained by chromatography, and we define and evaluate acceptance-sampling plans under this distributional setup for lots of large dimension. Some technical results associated with the construction and evaluation of such sampling plans are provided as well as an algorithm for an easy implementation of the sampling plan that exhibits the best performance.
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Research Interests: Medicine and Estimation
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In extreme value theory, any second-order parameter is an important parameter that measures the speed of convergence of the sequence of maximum values, linearly normalized, towards its limit law. In this paper we study a new estimator of... more
In extreme value theory, any second-order parameter is an important parameter that measures the speed of convergence of the sequence of maximum values, linearly normalized, towards its limit law. In this paper we study a new estimator of a shape second-order parameter under a third-order framework.
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A class of partially reduced-bias estimators of a positive extreme value index (EVI), related to a mean-of-order- p class of EVI-estimators, is introduced and studied both asymptotically and for finite samples through a Monte-Carlo... more
A class of partially reduced-bias estimators of a positive extreme value index (EVI), related to a mean-of-order- p class of EVI-estimators, is introduced and studied both asymptotically and for finite samples through a Monte-Carlo simulation study. A comparison between this class and a representative class of minimum-variance reduced-bias (MVRB) EVI-estimators is further considered. The MVRB EVI-estimators are related to a direct removal of the dominant component of the bias of a classical estimator of a positive EVI, the Hill estimator, attaining as well minimal asymptotic variance. Heuristic choices for the tuning parameters p and k , the number of top order statistics used in the estimation, are put forward, and applied to simulated and real data.
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Asymptotic properties of the statistic proposed by Gum-bel. Wn = {max(Xi) − med(Xi)}/{med(Xi) −min(Xi)}, are obtained for testing the shape parameter k = 0, in von Mises-Jenkinson form. Similar results are obtained for a ratio of... more
Asymptotic properties of the statistic proposed by Gum-bel. Wn = {max(Xi) − med(Xi)}/{med(Xi) −min(Xi)}, are obtained for testing the shape parameter k = 0, in von Mises-Jenkinson form. Similar results are obtained for a ratio of variances test statistic modified from one suggested by Jenkinson. Comparison is made; as could be expected Gumbel statistic turns out to be the better one.
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Research Interests: Geography and Statistics
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Let X denote a sample from a multivariate Generalized Extreme Value - GEV(6') - model. In this paper asymptotic properties of Gumbel type statistics - which properly balance both the upper and lower tail - are derived and asymptotic... more
Let X denote a sample from a multivariate Generalized Extreme Value - GEV(6') - model. In this paper asymptotic properties of Gumbel type statistics - which properly balance both the upper and lower tail - are derived and asymptotic properties of such statistics for testing H,: 0 = 0 in the multivariate GEV(0) model are obtained. A likelihood ratio test for H,,: 0 = 0 is also developed. A suitable algorithm for obtaining the maximum likelihood estimates of the unknown parameters is implemented. Comparison of tests is made through simulation methods.
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Under a semi-parametric framework, we consider second-order minimum-variance reduced-bias (MVRB) estimators of a positive extreme value index, the primary parameter in Statistics of Extremes, and associated estimation of the Value at Risk... more
Under a semi-parametric framework, we consider second-order minimum-variance reduced-bias (MVRB) estimators of a positive extreme value index, the primary parameter in Statistics of Extremes, and associated estimation of the Value at Risk (V aR) at a level p, the size of the loss occurred with a small probability p. For these MVRB estimators, we propose the use of bootstrap computer-intensive methods for the adaptive choice of thresholds. Applications in the elds of insurance
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The extreme value index characterizes the tail behaviour of a distribution, and indicates the size and frequency of certain extreme events under a given probability model. In this work, we are interested in improvements attained through... more
The extreme value index characterizes the tail behaviour of a distribution, and indicates the size and frequency of certain extreme events under a given probability model. In this work, we are interested in improvements attained through the reduction of bias of the extreme value index estimators related to Lehmer’s mean of the log-excesses. A comparison with other reduced bias estimators, namely the corrected-Hill estimator, in Caeiro et al. (Revstat 3(2):111–136, 2005), is also performed.