SIMULATION TECHNIQUES AND APPROXIMATED DISTRIBUTION OF AN EXTENDED GAMMA PROCESS

Zeina Al Masry (1) , Sophie Mercier (1) , Ghislain Verdier (1)

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

Many research deals with the standard Gamma process to model the evolution of the cumulative deterioration of a system with time. When the variance-to-mean ratio of the system deterioration level varies with time, the standard Gamma process is not convenient anymore because it provides a constant ratio. A way to overcome this restriction is to consider the extended version of a Gamma process proposed by Cinlar [1980]. However, based on its technic-ity, the use of such a process for applicative purpose requires the preliminary development of technical tools. In this paper, we propose methods to simulate its paths and approximate its cumulative distribution function, as a first step.

Mots clés: Degradation; Process with independent increments; Series representation; Inverse Laplace transform; Post-Widder formula

Domaines: Probabilités [math.PR]

Zeina Al Masry, Sophie Mercier, Ghislain Verdier. SIMULATION TECHNIQUES AND APPROXIMATED DISTRIBUTION OF AN EXTENDED GAMMA PROCESS. MMR 2015: Ninth International Conference on Mathematical Methods in Reliability, 2015, Tokyo, Japan. ⟨hal-01355148⟩