Implementing Markovian models for extendible Marshall–Olkin distributions

Abstract: We derive a novel stochastic representation of exchangeable Marshall–Olkin distributions based on their death-counting processes. We show that these processes are Markov. Furthermore, we provide a numerically stable approximation of their infinitesimal generator matrices in the extendible case. This approach uses integral representations of Bernstein functions to calculate the generator’s first row, and then uses a recursion to calculate the remaining rows. Combining the Markov representation with the numerically stable approximation of corresponding generators allows us to sample extendible Marshall–Olkin distributions with a flexible simulation algorithm derived from known Markov sampling strategies. Finally, we benchmark an implementation of this Markov-based simulation algorithm against alternative simulation algorithms based on the Lévy frailty model, the Arnold model, and the exogenous shock model.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Implementing Markovian models for extendible Marshall–Olkin distributions ; volume:10 ; number:1 ; year:2022 ; pages:308-343 ; extent:36 ; Dependence modeling ; 10, Heft 1 (2022), 308-343 (gesamt 36)

Contributors, Places and Time

• Creator: Sloot, Henrik

Further information

• DOI: 10.1515/demo-2022-0151
• URN: urn:nbn:de:101:1-2022121713055229706409
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 15.08.2025, 7:39 AM CEST