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Parameter Estimation of Discrete Multivariate Phase-Type Distributions

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  • Qi-Ming He

    (University of Waterloo)

  • Jiandong Ren

    (University of Western Ontario)

Abstract

This paper considers parameter estimation of a class of discrete multi-variate phase-type distributions (DMPH). Such discrete phase-type distributions are based on discrete Markov chains with marked transitions introduced by He and Neuts (Stoch Process Appl 74(1):37–52, 1998) and is a generalization of the discrete univariate phase–type distributions. Properties of the DMPHs are presented. An EM-algorithm is developed for estimating the parameters for DMPHs. A number of numerical examples are provided to address some interesting parameter selection issues and to show possible applications of DMPHs.

Suggested Citation

  • Qi-Ming He & Jiandong Ren, 2016. "Parameter Estimation of Discrete Multivariate Phase-Type Distributions," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 629-651, September.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:3:d:10.1007_s11009-015-9442-y
    DOI: 10.1007/s11009-015-9442-y
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    References listed on IDEAS

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    1. V. G. Kulkarni, 1989. "A New Class of Multivariate Phase Type Distributions," Operations Research, INFORMS, vol. 37(1), pages 151-158, February.
    2. He, Qi-Ming & Neuts, Marcel F., 1998. "Markov chains with marked transitions," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 37-52, May.
    3. Alexander Herbertsson, 2011. "Modelling default contagion using multivariate phase-type distributions," Review of Derivatives Research, Springer, vol. 14(1), pages 1-36, April.
    4. David Assaf & Naftali A. Langberg & Thomas H. Savits & Moshe Shaked, 1984. "Multivariate Phase-Type Distributions," Operations Research, INFORMS, vol. 32(3), pages 688-702, June.
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    Cited by:

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    2. Bladt, Martin & Yslas, Jorge, 2023. "Robust claim frequency modeling through phase-type mixture-of-experts regression," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 1-22.

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