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Parametric inference in a perturbed gamma degradation process

Author

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  • Laurent Bordes
  • Christian Paroissin
  • Ali Salami

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.

Suggested Citation

  • Laurent Bordes & Christian Paroissin & Ali Salami, 2016. "Parametric inference in a perturbed gamma degradation process," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(9), pages 2730-2747, May.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:9:p:2730-2747
    DOI: 10.1080/03610926.2014.892133
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    Cited by:

    1. Song, Kai & Shi, Jian & Yi, Xiaojian, 2020. "A time-discrete and zero-adjusted gamma process model with application to degradation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    2. Nicola Esposito & Agostino Mele & Bruno Castanier & Massimiliano Giorgio, 2023. "A new gamma degradation process with random effect and state-dependent measurement error," Journal of Risk and Reliability, , vol. 237(5), pages 868-885, October.
    3. Yaping Li & Enrico Zio & Ershun Pan, 2021. "An MEWMA-based segmental multivariate hidden Markov model for degradation assessment and prediction," Journal of Risk and Reliability, , vol. 235(5), pages 831-844, October.
    4. Xudan Chen & Guoxun Ji & Xinli Sun & Zhen Li, 2019. "Inverse Gaussian–based model with measurement errors for degradation analysis," Journal of Risk and Reliability, , vol. 233(6), pages 1086-1098, December.

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