Séance Séminaire

Séminaire de Probabilités et Statistique

Early detection of emergent events based on records and extremal process approach

Let $\{ S_n : n \geq 0 \}$ be a real renewal process representing the successive arrival times of some event (ex.: clinical case of an infectious disease). We wish to test that if the first observed events are sporadic (hypothesis H0) (the interarrival times $\{ \Delta S_k : k \leq n \}$ are i.i.d.), or emergent (hypothesis H1). We test H0 against H1, first by using the statistic of the number of upper records among $(X_k)$, where $X_k=(\Delta S_k)^{-1}$, second by the extremal process R(t) . We apply both types of methods on the real data (ex: BSE disease).