Summary
The present paper is concerned with the estimation of the transition distributions of a Markov renewal process with finitely many states. A natural estimator of the transition distributions is defined and shown to be consistent. Limiting distributions of this estimator are derived. A density for a Markov renewal process is developed to permit the definition of maximum likelihood estimators for a renewal process and for a Markov renewal process.
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Moore, E.H., Pyke, R. Estimation of the transition distributions of a Markov renewal process. Ann Inst Stat Math 20, 411–424 (1968). https://doi.org/10.1007/BF02911654
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DOI: https://doi.org/10.1007/BF02911654