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Stochastic comparisons and ageing properties of an extended gamma process

Part of: Special processes Stochastic processes Distribution theory - Probability

Published online by Cambridge University Press:  25 February 2021

Zeina Al Masry Open the ORCID record for Zeina Al Masry [Opens in a new window] ,
Sophie Mercier Open the ORCID record for Sophie Mercier [Opens in a new window]  and
Ghislain Verdier
Zeina Al Masry*
Affiliation:
FEMTO-ST, Univ. Bourgogne Franche-Comté, CNRS, ENSMM
Sophie Mercier*
Affiliation:
Université de Pau et des Pays de l’Adour, E2S UPPA, CNRS, LMAP, Pau, France
Ghislain Verdier*
Affiliation:
Université de Pau et des Pays de l’Adour, E2S UPPA, CNRS, LMAP, Pau, France
*
*Postal address: FEMTO-ST, Université Bourgogne Franche-Comté, CNRS, ENSMM, Besançon Cedex 25000, France. Email address: [email protected]
**Postal address: Université de Pau et des Pays de l’Adour, E2S UPPA, CNRS, LMAP, Pau 64000, France.
**Postal address: Université de Pau et des Pays de l’Adour, E2S UPPA, CNRS, LMAP, Pau 64000, France.
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Abstract

Extended gamma processes have been seen as a flexible extension of standard gamma processes in the recent reliability literature, for the purpose of cumulative deterioration modeling. The probabilistic properties of the standard gamma process have been well explored since the 1970s, whereas those of its extension remain largely unexplored. In particular, stochastic comparisons between degradation levels modeled by standard gamma processes and ageing properties for the corresponding level-crossing times are now well understood. The aim of this paper is to explore similar properties for extended gamma processes and see which ones can be broadened to this new context. As a by-product, new stochastic comparisons for convolutions of gamma random variables are also obtained.

Keywords

Reliability theorycumulative deteriorationstandard gamma processextended gamma processstochastic orderageing properties

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 60E15: Inequalities; stochastic orderings 60G51: Processes with independent increments; L'evy processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 58 , Issue 1 , March 2021 , pp. 140 - 163
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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