On the Mixed Extended Generalized Pólya Process and Its Stochastic Intensity Paradox

A new class of counting processes generated by the mixture of the extended generalized Pólya process is defined and its properties are studied. The general form of the corresponding stochastic intensity is derived. Specifying geometric, negative binomial, Poisson, and binomial distributions as the m...

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Bibliographic Details
Published inMethodology and computing in applied probability Vol. 27; no. 3; p. 66
Main Authors Cha, Ji Hwan, Finkelstein, Maxim
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2025
Springer Nature B.V
Subjects
Business and Management
Debugging
Economics
Electrical Engineering
Life Sciences
Mathematics and Statistics
Random variables
Software
Statistics
Mixing distribution
Secondary 62P30
Extended generalized Pólya process
Primary 60K10
Failure process
Stochastic intensity
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Summary:A new class of counting processes generated by the mixture of the extended generalized Pólya process is defined and its properties are studied. The general form of the corresponding stochastic intensity is derived. Specifying geometric, negative binomial, Poisson, and binomial distributions as the mixing distributions, four parametric classes of counting processes are defined and stochastically characterized. It is shown that relevant monotonicity properties of the corresponding stochastic intensities do not follow ‘direct intuition’ and can dramatically change depending on the mixing distribution. The practical meaning of the considered parametric models is also interpreted from the reliability point of view.
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ISSN:1387-5841
1573-7713
DOI:10.1007/s11009-025-10195-1