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The estimation of phase-type related functionals using Markov chain Monte Carlo methods

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  • Mogens Bladt
  • Antonio Gonzalez
  • Steffen L. Lauritzen

Abstract

In this paper we present a method for estimation of functionals depending on one or several phase-type distributions. This could for example be the ruin probability in a risk reserve process where claims are assumed to be of phase-type. The proposed method uses a Markov chain Monte Carlo simulation to reconstruct the Markov jump processes underlying the phase-type variables in combination with Gibbs sampling to obtain a stationary sequence of phase-type probability measures from the posterior distribution of these given the observations. This enables us to find quantiles of posterior distributions of functionals of interest, thereby representing estimation uncertainty in a flexible way. We compare our estimates to those obtained by the method of maximum likelihood and find a good agreement. We illustrate the statistical potential of the method by estimating ruin probabilities in simulated examples.

Suggested Citation

  • Mogens Bladt & Antonio Gonzalez & Steffen L. Lauritzen, 2003. "The estimation of phase-type related functionals using Markov chain Monte Carlo methods," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2003(4), pages 280-300.
    • Handle: RePEc:taf:sactxx:v:2003:y:2003:i:4:p:280-300
    DOI: 10.1080/03461230110106435
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    Cited by:

    1. Bo Henry Lindqvist, 2023. "Phase-type models for competing risks, with emphasis on identifiability issues," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 318-341, April.
    2. Hobolth, Asger & Rivas-González, Iker & Bladt, Mogens & Futschik, Andreas, 2024. "Phase-type distributions in mathematical population genetics: An emerging framework," Theoretical Population Biology, Elsevier, vol. 157(C), pages 14-32.

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