Implementing Markovian models for extendible Marshall–Olkin distributions

Sloot Henrik ()
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Sloot Henrik: Technical University of Munich, Parkring 11, 85748 Garching-Hochbrück, Germany

Dependence Modeling, 2022, vol. 10, issue 1, 308-343

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.

Keywords: Marshall–Olkin distribution; sampling algorithm; Markov processes; exchangeability; lack of memory; multivariate survival analysis (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:10:y:2022:i:1:p:308-343:n:1

DOI: 10.1515/demo-2022-0151

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