Data Geometry and Extreme Value Distribution

Algèbre de Clifford Algèbre de Grassmann Graphe géométrique stochastique Blade groups Mobile ad hoc Network protocole de routage Distribution GEV

Authors

  • 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
    alahassan@dms.umontreal.ca
    Department of Mathematics and Statistics, University of Montreal, Montreal, Canada
July 17, 2021

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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.