Parametric inference in a perturbed gamma degradation process

Abstract

We consider a degradation model which is the sum of two independent processes: an homogeneous gamma process and a Brownian motion. This model is called perturbed gamma process. Based on independent copies of the perturbed gamma process observed at irregular instants we propose to estimate the unknown parameters of the model using the moment method. Some general conditions allow to derive the asymptotic behavior of the estimators. We also show that these general conditions are fulfilled for some specific observation schemes. Finally, we illustrate our method by a numerical study and an application to a real data set.

Keywords:

• Wiener process
• Gamma process
• Moments method
• Consistency
• asymptotic normality

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F10
• 62F12
• 62N05

Acknowledgment

We would like to thank the two anonymous referees for providing us with constructive comments and suggestions.