Parametric inference in a perturbed gamma degradation process

Laurent Bordes (1) , Christian Paroissin (1) , Ali Salami (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

We consider the gamma process perturbed by a Brownian motion (independent of the gamma process) as a degradation model. Parameters estimation is studied here. We assume that $n$ independent items are observed at irregular instants. From these observations, we estimate the parameters using the moments method. Then, we study the asymptotic properties of the estimators. Furthermore we derive some particular cases of items observed at regular or non-regular instants. Finally, some numerical simulations and two real data applications are provided to illustrate our method.

Mots clés: gamma process; Wiener process; method of moments; consistency; asymptotic normality

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Laurent Bordes, Christian Paroissin, Ali Salami. Parametric inference in a perturbed gamma degradation process. 2010. ⟨hal-00481928⟩