Extremal properties and risk indicators of dietary risk assessment models with heavy-tailed intakes

Charles Tillier (1)

1 MODAL'X - Modélisation aléatoire de Paris X

The objective of this paper is twofold: to investigate the extremal behavior of a class of stochastic processes and to introduce new models that could be useful in risk theory. We focus on a dietary risk assessment context and we work under the assumption of heavy-tailed intakes. Precisely, we study the extremal properties of an extension of the so-called Shot Noise Processes by characterising two risk indicators: the tail behavior and the extremal index. For the sake of applicability, we suggest three models, which stem from KDEM process studied in Bertail et al. (2008) , that aim at representing the evolution of a contaminant in the human body through time. We also propose a way to add dependence between the intakes. Finally, we present few simulations to check the consistency of our results.

Mots clés: Risk indicators; Extreme Value Theory; Dietary risk assessment; Heavy-tailed phenomena

Domaines: Statistiques [stat]; Applications [stat.AP]; Sciences du Vivant [q-bio]; Santé publique et épidémiologie

Charles Tillier. Extremal properties and risk indicators of dietary risk assessment models with heavy-tailed intakes. 2018. ⟨hal-01741202⟩