SIMULATION TECHNIQUES AND APPROXIMATED DISTRIBUTION OF AN EXTENDED GAMMA PROCESS
Résumé
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.
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