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Normalisation functions and the reliability of the estimation of the GEV return level: A comparative study based on CAC 40 index

Mohammadine Belbachir, Guei Cyrille Okou, Labloul Bouchra

Abstract



Much work has developed the estimated return level for linear normalization in the extreme value theory (EVT). In this article, we propose a theoretical approach based on the function of Von Mises to estimate the return level for the EVT in the case of the non linear normalization (power normalization). Algorithms based on numerical approaches have been developed to estimate the extreme quantiles and return periods of GEV models in the case
of linear and non-linear normalization. The results show that the non-linear normalization model (GEVP) provide more realistic estimations of return periods. The finding was highlighted in working with the CAC 40 index and the parameters are estimated by the maximum likelihood method.

Keywords


extreme value theory , linear normalization, non linear normalization, return period, extreme quantiles.

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