Estimation in Stationary Markov Renewal Processes, with Application to Earthquake Forecasting in Turkey

  • Enrique E. AlvarezEmail author
Original Article


Consider a process in which different events occur, with random inter-occurrence times. In Markov renewal processes as well as in semi-Markov processes, the sequence of events is a Markov chain and the waiting distributions depend only on the types of the last and the next event. Suppose that the state-space is finite and that the process started far in the past, achieving stationary. Weibull distributions are proposed for the waiting times and their parameters are estimated jointly with the transition probabilities through maximum likelihood, when one or several realizations of the process are observed over finite windows. The model is illustrated with data of earthquakes of three types of severity that occurred in Turkey during the 20th century.


earthquakes marked point process Markov renewal process semi-Markov process stationarity window censoring 


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of ConnecticutStorrsUSA

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