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Approximate Simulation Techniques and Distribution of an Extended Gamma Process

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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.

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Authors and Affiliations

  1. Laboratoire de Mathématiques et de leurs Applications - Pau (UMR CNRS 5142), Université de Pau et des Pays de l’Adour, Bâtiment IPRA, Avenue de l’Université, F-64013, PAU Cedex, France

    Zeina Al Masry, Sophie Mercier & Ghislain Verdier

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  1. Zeina Al Masry
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  2. Sophie Mercier
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  3. Ghislain Verdier
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Correspondence to Zeina Al Masry.

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Al Masry, Z., Mercier, S. & Verdier, G. Approximate Simulation Techniques and Distribution of an Extended Gamma Process. Methodol Comput Appl Probab 19, 213–235 (2017). https://doi.org/10.1007/s11009-015-9474-3

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  • DOI: https://doi.org/10.1007/s11009-015-9474-3

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