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Generalized method of moments for an extended gamma process

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  • Z. Al Masry
  • S. Mercier
  • G. Verdier

Abstract

In reliability theory, a widely used process to model the phenomena of the cumulative deterioration of a system over time is the standard gamma process (SGP). Based on several restrictions, such as a constant variance-to-mean ratio, this process is not always a suitable choice to describe the deterioration. A way to overcome these restrictions is to use an extended version of the gamma process introduced by Cinlar (1980), which is characterized by shape and scale functions. In this article, the aim is to propose statistical methods to estimate the unknown parameters of parametric forms of the shape and scale functions. We here develop two generalized methods of moments (Hansen 1982), based either on the moments or on the Laplace transform of an extended gamma process. Asymptotic properties are provided and a Wald-type test is derived, which allows to test SGPs against extended ones with a specific parametric shape function. Also, the performance of the proposed estimation methods is illustrated on simulated and real data.

Suggested Citation

  • Z. Al Masry & S. Mercier & G. Verdier, 2018. "Generalized method of moments for an extended gamma process," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(15), pages 3687-3714, August.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:15:p:3687-3714
    DOI: 10.1080/03610926.2017.1361988
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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).

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