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Article Dans Une Revue Methodology and Computing in Applied Probability Année : 2019

Extensions of the Generalized Pólya Process

Résumé

A new self-exciting counting process is here considered, which extends the generalized Pólya process introduced by Cha [Advances in Applied Probability, 46, 1148-1171 (2014)]. Contrary to Cha's original model, where the intensity of the process (linearly) increases at each jump time, the extended version allows for more flexibility in the dependence between the point-wise intensity of the process at some time t and the number of already observed jumps. This allows the " extended Pólya process " to be appropriate, e.g., for describing successive failures of a system subject to imperfect but effective repairs, where the repair can lower the intensity of the underlying counting process. Probabilistic properties of the new process are studied (construction from a homogeneous pure-birth process, conditions of non explosion, computation of distributions, convergence of a sequence of such processes, ...) and its connection with Generalized Order Statistics is highlighted. Positive dependence properties are next explored. Finally, the maximum likelihood method is considered in a parametric setting and tested on a few simulated data sets, to highlight the practical use of the new process in an application context.
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Dates et versions

hal-01861268 , version 1 (24-08-2018)

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Francisco Germán Badía, Sophie Mercier, Carmen Sangüesa. Extensions of the Generalized Pólya Process. Methodology and Computing in Applied Probability, 2019, 21 (4), pp.1057-1085. ⟨10.1007/s11009-018-9663-y⟩. ⟨hal-01861268⟩
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