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

Ji Hwan Cha () and Maxim Finkelstein ()
Additional contact information
Ji Hwan Cha: Ewha Womans University
Maxim Finkelstein: University of the Free State

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 3, 1-18

Abstract: Abstract 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.

Keywords: Extended generalized Pólya process; Stochastic intensity; Mixing distribution; Failure process; Primary 60K10; Secondary 62P30 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-025-10195-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:27:y:2025:i:3:d:10.1007_s11009-025-10195-1

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-025-10195-1

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().