Publications

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2023
Caeiro, F., & Mateus A. (2023).  A New Class of Generalized Probability-Weighted Moment Estimators for the Pareto Distribution. Mathematics. 11, 1076., feb, Number 5: {MDPI} {AG} AbstractWebsite
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2022
Caeiro, F., Henriques-Rodrigues L. {\'ı}gia, & Gomes I. M. (2022).  The Use of Generalized Means in the Estimation of the Weibull Tail Coefficient. (Anil Kumar, Ed.).Computational and Mathematical Methods. 2022, 1–12., jun: Hindawi Limited AbstractWebsite
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Mateus, A., & Caeiro F. (2022).  Improved Shape Parameter Estimation for the Three-Parameter Log-Logistic Distribution. (Qichun Zhang, Ed.).Computational and Mathematical Methods. 2022, 1–13., feb: Hindawi Limited AbstractWebsite
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Mateus, A., & Caeiro F. (2022).  Confidence Intervals for the Shape Parameter of a Pareto Distribution. AIP Conference Proceedings. 2425, Abstract
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Caeiro, F., & Mateus A. (2022).  Exponential versus Generalized Exponential Distribution: a Computational Study. AIP Conference Proceedings. 2425, Abstract
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Cabral, I., Caeiro F., & Gomes M. I. (2022).  On the comparison of several classical estimators of the extreme value index. Communications in Statistics - Theory and Methods. 51, 179-196., Number 1 Abstract
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Caeiro, F. (2022).  Preface of the Session ?Computational Statistical Methods?. AIP Conference Proceedings. 2425, Abstract
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2021
Caeiro, F., Mateus A., & Soltane L. (2021).  A class of weighted Hill estimators. Computational and Mathematical Methods. , may: Wiley AbstractWebsite
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2020
Mateus, A., & Caeiro F. (2020).  A new class of estimators for the shape parameter of a Pareto model. Computational and Mathematical Methods. , nov: Wiley AbstractWebsite
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Caeiro, F., Henriques-Rodrigues L. {\'ı}gia, Gomes I. M., & Cabral I. (2020).  Minimum-variance reduced-bias estimation of the extreme value index: A theoretical and empirical study. Computational and Mathematical Methods. , may: Wiley AbstractWebsite
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Gomes, M. I., Caeiro F., Figueiredo F., Henriques-Rodrigues L., & Pestana D. (2020).  Corrected-Hill versus partially reduced-bias value-at-risk estimation. Communications in Statistics: Simulation and Computation. 49, 867-885., Number 4 Abstract
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Penalva, H., Ivette Gomes M., Caeiro F., & Manuela Neves M. (2020).  A couple of non reduced bias generalized means in extreme value theory: An asymptotic comparison. Revstat Statistical Journal. 18, 281-298., Number 3 Abstract
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Penalva, H., Gomes M. I., Caeiro F., & Neves M. M. (2020).  Lehmer{'}s mean-of-order-p extreme value index estimation: a simulation study and applications. Journal of Applied Statistics. 47, 2825-2845., Number 13-15 Abstract
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Gomes, M. I., Caeiro F., Figueiredo F., Henriques-Rodrigues L., & Pestana D. (2020).  Reduced-bias and partially reduced-bias mean-of-order-p value-at-risk estimation: a Monte-Carlo comparison and an application. Journal of Statistical Computation and Simulation. 90, 1735-1752., Number 10 Abstract
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2019
Caeiro, F., Henriques-Rodrigues L. {\'ı}gia, & Gomes D. P. (2019).  A simple class of reduced bias kernel estimators of extreme value parameters. Computational and Mathematical Methods. e1025., apr: Wiley AbstractWebsite
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Caeiro, F., & Henriques-Rodrigues L. (2019).  Reduced-bias kernel estimators of a positive extreme value index. Mathematical Methods in the Applied Sciences. 42, 5867-5880., Number 17 Abstract
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2018
Caeiro, F., & Mateus A. (2018).  Empirical Power Study of the Jackson Exponentiality Test. Demography and Health Issues. 225–235.: Springer International Publishing Abstract
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Mateus, A., & Caeiro F. (2018).  Exact and Approximate Probabilities for the Null Distribution of Bartels Randomness Test. Contributions to Statistics. 227–240.: Springer International Publishing Abstract
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Caeiro, F., Cabral I., & Gomes I. M. (2018).  Improving Asymptotically Unbiased Extreme Value Index Estimation. Contributions to Statistics. 155–163.: Springer International Publishing Abstract
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2016
Caeiro, F. A. G. G., Gomes I. M., & Henriques-Rodrigues L. (2016).  A location-invariant probability weighted moment estimation of the Extreme Value Index. International Journal of Computer Mathematics. 93(4), 676 - 695., 2016/4/2 AbstractWebsite

The peaks over random threshold (PORT) methodology and the Pareto probability weighted moments (PPWM) of the largest observations are used to build a class of location-invariant estimators of the Extreme Value Index (EVI), the primary parameter in statistics of extremes. The asymptotic behaviour of such a class of EVI-estimators, the so-called PORT-PPWM EVI-estimators, is derived, and an alternative class of location-invariant EVI-estimators, the generalized Pareto probability weighted moments (GPPWM) EVI-estimators is considered as an alternative. These two classes of estimators, the PORT-PPWM and the GPPWM, jointly with the classical Hill EVI-estimator and a recent class of minimum-variance reduced-bias estimators are compared for finite samples, through a large-scale Monte-Carlo simulation study. An adaptive choice of the tuning parameters under play is put forward and applied to simulated and real data sets.The peaks over random threshold (PORT) methodology and the Pareto probability weighted moments (PPWM) of the largest observations are used to build a class of location-invariant estimators of the Extreme Value Index (EVI), the primary parameter in statistics of extremes. The asymptotic behaviour of such a class of EVI-estimators, the so-called PORT-PPWM EVI-estimators, is derived, and an alternative class of location-invariant EVI-estimators, the generalized Pareto probability weighted moments (GPPWM) EVI-estimators is considered as an alternative. These two classes of estimators, the PORT-PPWM and the GPPWM, jointly with the classical Hill EVI-estimator and a recent class of minimum-variance reduced-bias estimators are compared for finite samples, through a large-scale Monte-Carlo simulation study. An adaptive choice of the tuning parameters under play is put forward and applied to simulated and real data sets.

Caeiro, F., Marques F. J., Mateus A., & Atal S. (2016).  A note on the Jackson exponentiality test. International Conference of Computational Methods in Sciences and Engineering 2016, ICCMSE 2016. 1790, , 2016/12/6: American Institute of Physics Inc. Abstract

In this paper we revisit the Jackson exponentiality test. We study and provide functions in R language to compute theoretical moments, the distribution function and quantiles of the statistic test. Approximations to the exact distribution function and quantiles are also provided and their precision discussed. In addition, we provide an application of the Jackson test to real data.In this paper we revisit the Jackson exponentiality test. We study and provide functions in R language to compute theoretical moments, the distribution function and quantiles of the statistic test. Approximations to the exact distribution function and quantiles are also provided and their precision discussed. In addition, we provide an application of the Jackson test to real data.

Cabral, I., Caeiro F., & Gomes I. M. (2016).  Reduced bias Hill estimators. International Conference of Computational Methods in Sciences and Engineering 2016, ICCMSE 2016. 1790, , 2016/12/6: American Institute of Physics Inc. Abstract

For heavy tails, classical extreme value index estimators, like the Hill estimator, are usually asymptotically biased. Consequently those estimators are quite sensitive to the number of top order statistics used in the estimation. The recent minimum-variance reduced-bias extreme value index estimators enable us to remove the dominant component of asymptotic bias and keep the asymptotic variance of the new estimators equal to the asymptotic variance of the Hill estimator. In this paper a new minimum-variance reduced-bias extreme value index estimator is introduced, and its non degenerate asymptotic behaviour is studied. A comparison with another important minimum-variance reduced-bias extreme value index estimator is also provided.For heavy tails, classical extreme value index estimators, like the Hill estimator, are usually asymptotically biased. Consequently those estimators are quite sensitive to the number of top order statistics used in the estimation. The recent minimum-variance reduced-bias extreme value index estimators enable us to remove the dominant component of asymptotic bias and keep the asymptotic variance of the new estimators equal to the asymptotic variance of the Hill estimator. In this paper a new minimum-variance reduced-bias extreme value index estimator is introduced, and its non degenerate asymptotic behaviour is studied. A comparison with another important minimum-variance reduced-bias extreme value index estimator is also provided.

Mateus, A., Caeiro F., Gomes D. P., & Sequeira I. J. (2016).  Statistical analysis of extreme river flows. International Conference of Computational Methods in Sciences and Engineering 2016, ICCMSE 2016. 1790, , 2016/12/6: American Institute of Physics Inc. Abstract

Floods are recurrent events that can have a catastrophic impact. In this work we are interested in the analysis of a data set of gauged daily flows from the Whiteadder Water river, Scotland. Using statistic techniques based on extreme value theory, we estimate several extreme value parameters, including extreme quantiles and return periods of high levels.Floods are recurrent events that can have a catastrophic impact. In this work we are interested in the analysis of a data set of gauged daily flows from the Whiteadder Water river, Scotland. Using statistic techniques based on extreme value theory, we estimate several extreme value parameters, including extreme quantiles and return periods of high levels.

Caeiro, F., Gomes I. M., Beirlant J., & de Wet T. (2016).  Mean-of-order p reduced-bias extreme value index estimation under a third-order framework. ExtremesExtremes. 19(4), 561 - 589., 2016/12/1 AbstractWebsite

Reduced-bias versions of a very simple generalization of the ‘classical’ Hill estimator of a positive extreme value index (EVI) are put forward. The Hill estimator can be regarded as the logarithm of the mean-of-order-0 of a certain set of statistics. Instead of such a geometric mean, it is sensible to consider the mean-of-order-p (MOP) of those statistics, with p real. Under a third-order framework, the asymptotic behaviour of the MOP, optimal MOP and associated reduced-bias classes of EVI-estimators is derived. Information on the dominant non-null asymptotic bias is also provided so that we can deal with an asymptotic comparison at optimal levels of some of those classes. Large-scale Monte-Carlo simulation experiments are undertaken to provide finite sample comparisons.Reduced-bias versions of a very simple generalization of the ‘classical’ Hill estimator of a positive extreme value index (EVI) are put forward. The Hill estimator can be regarded as the logarithm of the mean-of-order-0 of a certain set of statistics. Instead of such a geometric mean, it is sensible to consider the mean-of-order-p (MOP) of those statistics, with p real. Under a third-order framework, the asymptotic behaviour of the MOP, optimal MOP and associated reduced-bias classes of EVI-estimators is derived. Information on the dominant non-null asymptotic bias is also provided so that we can deal with an asymptotic comparison at optimal levels of some of those classes. Large-scale Monte-Carlo simulation experiments are undertaken to provide finite sample comparisons.