000148166 001__ 148166 000148166 005__ 20250115151521.0 000148166 0247_ $$2doi$$a10.1007/s11009-018-9663-y 000148166 0248_ $$2sideral$$a107580 000148166 037__ $$aART-2019-107580 000148166 041__ $$aeng 000148166 100__ $$0(orcid)0000-0002-6651-3306$$aBadía, F.G.$$uUniversidad de Zaragoza 000148166 245__ $$aExtensions of the Generalized Pólya Process 000148166 260__ $$c2019 000148166 5060_ $$aAccess copy available to the general public$$fUnrestricted 000148166 5203_ $$aA 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. 000148166 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E64$$9info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2015-63978-P 000148166 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000148166 590__ $$a0.809$$b2019 000148166 591__ $$aSTATISTICS & PROBABILITY$$b81 / 124 = 0.653$$c2019$$dQ3$$eT2 000148166 592__ $$a0.569$$b2019 000148166 593__ $$aStatistics and Probability$$c2019$$dQ2 000148166 593__ $$aMathematics (miscellaneous)$$c2019$$dQ2 000148166 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000148166 700__ $$aMercier, S. 000148166 700__ $$0(orcid)0000-0002-7099-7665$$aSangüesa, C.$$uUniversidad de Zaragoza 000148166 7102_ $$12007$$2265$$aUniversidad de Zaragoza$$bDpto. Métodos Estadísticos$$cÁrea Estadís. Investig. Opera. 000148166 773__ $$g21 (2019), 1057 – 1085$$pMethodol. Comput. Appl. Probab.$$tMETHODOLOGY AND COMPUTING IN APPLIED PROBABILITY$$x1387-5841 000148166 8564_ $$s449434$$uhttps://zaguan.unizar.es/record/148166/files/texto_completo.pdf$$yPostprint 000148166 8564_ $$s1302092$$uhttps://zaguan.unizar.es/record/148166/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000148166 909CO $$ooai:zaguan.unizar.es:148166$$particulos$$pdriver 000148166 951__ $$a2025-01-15-15:14:34 000148166 980__ $$aARTICLE