Extensions of the Generalized Pólya Process

Badía, F.G. (Universidad de Zaragoza) ; Mercier, S. ; Sangüesa, C. (Universidad de Zaragoza)

Resumen: A new self-exciting counting process is here considered, which extends the generalized Pólya process introduced by Cha (Adv Appl Probab 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.

Idioma: Inglés

DOI: 10.1007/s11009-018-9663-y

Año: 2019

Publicado en: METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY 21 (2019), 1057 – 1085
ISSN: 1387-5841

Factor impacto JCR: 0.809 (2019)

Categ. JCR: STATISTICS & PROBABILITY rank: 81 / 124 = 0.653 (2019) - Q3 - T2

Factor impacto SCIMAGO: 0.569 - Statistics and Probability (Q2) - Mathematics (miscellaneous) (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E64
Financiación: info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2015-63978-P

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Estadís. Investig. Opera. (Dpto. Métodos Estadísticos)