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On identifiability of MAP processes

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

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 & Wiper, Michael Peter & Lillo Rodríguez, Rosa Elvira, 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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    Keywords

    Identifiability problems;

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