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Data Geometry and Extreme Value Distribution

Author

Listed:
  • Mamadou Cisse

    (National School of Statistics and Economical Analysis, University of Cheikh Anta Diop, Dakar, Senegal)

  • Aliou Diop

    (Gaston Berger University of Saint Louis, Saint Louis, Senegal)

  • Souleymane Bognini

    (National School of Statistics and Economical Analysis, University of Cheikh Anta Diop, Dakar, Senegal)

  • Nonvikan Karl-Augustt ALAHASSA

    (Department of Mathematics and Statistics, University of Montreal, Montreal, Canada)

Abstract

In extreme values theory, there exist two approaches about data treatment: block maxima and peaks-over-threshold (POT) methods, which take in account data over a fixed value. But, those approaches are limited. We show that if a certain geometry is modeled with stochastic graphs, probabilities computed with Generalized Extreme Value (GEV) Distribution can be deflated. In other words, taking data geometry in account change extremes distribution. Otherwise, it appears that if the density characterizing the states space of data system is uniform, and if the quantile studied is positive, then the Weibull distribution is insensitive to data geometry, when it is an area attraction, and the Fréchet distribution becomes the less inflationary.

Suggested Citation

  • Mamadou Cisse & Aliou Diop & Souleymane Bognini & Nonvikan Karl-Augustt ALAHASSA, 2021. "Data Geometry and Extreme Value Distribution," Journal of Mathematics and Statistics Studies, Al-Kindi Center for Research and Development., vol. 2(2), pages 06-15, June.
    • Handle: RePEc:alk:jmss00:v:2:y:2021:i:2:id:1875
    DOI: 10.32996/jmss.2021.2.2.2
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