Approximate Simulation Techniques and Distribution of an Extended Gamma Process

Zeina Al Masry (), Sophie Mercier () and Ghislain Verdier ()
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Zeina Al Masry: Université de Pau et des Pays de l’Adour
Sophie Mercier: Université de Pau et des Pays de l’Adour
Ghislain Verdier: Université de Pau et des Pays de l’Adour

Methodology and Computing in Applied Probability, 2017, vol. 19, issue 1, 213-235

Abstract: Abstract In reliability theory, many papers use a standard Gamma process to model the evolution of the cumulative deterioration of a system over time. When the variance-to-mean ratio of the system deterioration level varies over time, the standard Gamma process is not convenient any more 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 (J Appl Probab 17:467–480, 1980). However, based on its technicality, the use of such a process for applicative purpose requires the preliminary development of technical tools for simulating its paths and for the numerical assessment of its distribution. This paper is devoted to these two points.

Keywords: Reliability; Degradation; Process with independent increments; Series representation; Inverse laplace transform; Post-Widder formula; Weighted Gamma process; MSC : 60G51; 60K10 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-015-9474-3

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