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On identifiability of MAP processes

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  • Ramírez Cobo, Josefa
  • Lillo Rodríguez, Rosa Elvira
  • Wiper, Michael Peter

Abstract

Two types of transitions can be found in the Markovian Arrival process or MAP: with and without arrivals. In transient transitions the chain jumps from one state to another with no arrival; in effective transitions, a single arrival occurs. We assume that in practice, only arrival times are observed in a MAP. This leads us to define and study the Effective Markovian Arrival process or E-MAP. In this work we define identifiability of MAPs in terms of equivalence between the corresponding E-MAPs and study conditions under which two sets of parameters induce identical laws for the observable process, in the case of 2 and 3-states MAP. We illustrate and discuss our results with examples.

Suggested Citation

  • Ramírez Cobo, Josefa & Lillo Rodríguez, Rosa Elvira & Wiper, Michael Peter, 2008. "On identifiability of MAP processes," DES - Working Papers. Statistics and Econometrics. WS ws084613, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws084613
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    References listed on IDEAS

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    1. Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
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    1. Ramírez Cobo, Josefa & Lillo Rodríguez, Rosa Elvira & Wiper, Michael Peter, 2009. "Non-identifiability of the two state Markovian Arrival process," DES - Working Papers. Statistics and Econometrics. WS ws097121, Universidad Carlos III de Madrid. Departamento de Estadística.

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    Keywords

    Batch Markovian Arrival process;

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