News, practical results and applications of the clustered-states Markovian Arrival Process

R. E. Lillo, Á. Díaz Pérez, P. Ramirez Cobo

The clustered-states Markovian Arrival Process is introduced as a point process derived from a MAP for dependent recurrence times data. It has been defined in response to the modeling of data related to the recurrence or death of patients with oncological diseases. Novel properties, closed-form expressions for the marginal and joint densities of the times between recurrences as well as results that reduce the computational time of process simulation are provided. Some computational issues regarding the sample sizes and the evaluation of the likelihood function are discussed. Finally, an MLE-based approach for statistical inference is presented with applications to the modeling of a real dataset.

Keywords: Stochastic Process, MAP, Inference.

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