148166 20250115151521.0 doi 10.1007/s11009-018-9663-y sideral 107580 ART-2019-107580 eng Badía, F.G. Universidad de Zaragoza (orcid)0000-0002-6651-3306 Extensions of the Generalized Pólya Process 2019 Access copy available to the general public Unrestricted 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. info:eu-repo/grantAgreement/ES/DGA/E64 info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2015-63978-P info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 0.809 2019 STATISTICS & PROBABILITY 81 / 124 = 0.653 2019 Q3 T2 0.569 2019 Statistics and Probability 2019 Q2 Mathematics (miscellaneous) 2019 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Mercier, S. Sangüesa, C. Universidad de Zaragoza (orcid)0000-0002-7099-7665 2007 265 Universidad de Zaragoza Dpto. Métodos Estadísticos Área Estadís. Investig. Opera. 21 (2019), 1057 – 1085 Methodol. Comput. Appl. Probab. METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY 1387-5841 449434 http://zaguan.unizar.es/record/148166/files/texto_completo.pdf Postprint 1302092 http://zaguan.unizar.es/record/148166/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:148166 articulos driver 2025-01-15-15:14:34 ARTICLE