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Methodology and Computing in Applied Probability

, Volume 18, Issue 3, pp 629–651 | Cite as

Parameter Estimation of Discrete Multivariate Phase-Type Distributions

  • Qi-Ming HeEmail author
  • Jiandong Ren
Article

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.

Keywords

Risk analysis Parameter estimation PH-distributions 

Mathematics Subject Classification (2010)

Primary: 60-08 Secondary: 60J22 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Management SciencesUniversity of WaterlooWaterlooCanada
  2. 2.Department of Statistical and Actuarial SciencesUniversity of Western OntarioLondonCanada

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