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![]() BÂCĂ, Adrian-Iulian. Extreme values modeling using the Gamma-Lognormal-Pareto three-spliced distribution. In: Conference on Applied and Industrial Mathematics: CAIM 2022, Ed. 29, 25-27 august 2022, Chişinău. Chișinău, Republica Moldova: Casa Editorial-Poligrafică „Bons Offices”, 2022, Ediţia a 29, p. 105. ISBN 978-9975-81-074-6. |
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Conference on Applied and Industrial Mathematics Ediţia a 29, 2022 |
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Conferința "Conference on Applied and Industrial Mathematics" 29, Chişinău, Moldova, 25-27 august 2022 | ||||||
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Pag. 105-105 | ||||||
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Rezumat | ||||||
Extreme value theory (EVT) is a field of probability and statistics dealing with models for extreme values. The study of extreme events is very important because, even if they rarely happen, extreme events can have a catastrophic impact once they happened. Therefore, EVT has applications in many fields such as climatology, hydrology, engineering, traffic prediction, finance, insurance, epidemics etc. When data exhibit high frequency of small to medium values and low frequency of large values, fitting a classical distribution might fail. This is why in the recent years, the study of spliced models gained a lot of interest in the development of univariate EVT models. This interest is due to the particular form of spliced models, which are defined from different distributions on distinct adjacent intervals. This particularity insures a better fit to specific data presenting extreme values. In contrast to the intensive study of two-spliced distributions, the case with more than two components is scarcely approached. In this paper, we introduce and study the three-spliced Gamma-LognormalPareto distribution. A special attention is paid to the estimation procedure, especially since the thresholds where such distributions change shape are considered unknown parameters, which makes the estimation more challenging. We illustrate the estimation procedure on simulated data. |
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