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Study of Temporal Point Process as a Renewal Process with the Distribution of Interevent Time is Exponential Family

Nurtiti Sunusi, Abd. Naser, A. Kresna J, Anna Islamiyati, Raupong


Study of inter events time is a part of temporal point process modeling. In this study, temporal point process is consider as a renewal process which is the inter event times have independent identity distributions. The conditional intensity of the process coincides with so called hazard rate. In this paper, we analyze hazard rate with assume that the distribution of inter events time of hazard rate is exponential family, that are exponential, Pareto, and Rayleigh. To estimate the parameter of hazard rate, Maximum Likelihood Estimates (MLE) method is used. The simulation of Conditional Intensity value is given at the end of the paper. The result shows that all of the distribution gives the hazard rate value are different.


Point Process, Renewal Process, Conditional Intensity, exponentially family distributed.

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