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Compound Poisson processes; hypothesis testing; parameter estimation; waiting time distributions; Polya process; statistical models for earthquake occurrences

Very little work has been done in generating alternatives to the Poisson process model. The work reported here deals with alternatives to the Poisson process model for the earthquakes and checks them using empirical data and the statistical hypothesis testing apparatus. The strategy used here for generating hypotheses is to compound the Poisson process. The parameter of the Poisson process is replaced by a random variable having prescribed density function. The density functions used are gamma, chi and extended (gamma/chi). The original distribution is then averaged out with respect to these density functions. For the compound Poisson processes the waiting time distributions for the future events are derived. As the parameters for the various statistical models for earthquake occurrences are not known, the problem is basically of composite hypothesis testing. One way of designing a test is to estimate these parameters and use them as true values. Momentmatching is used here to estimate the parameters. The results of hypothesis testing using data from Hindukush and North East India are presented.

Naveen¹ P S Moharir¹ V K Gaur^{1 2}

1. Department of Earth Sciences, University of Roorkee, Roorkee - 247 667, India
2. National Geophysical Research Institute, Uppal Road, Hyderabad - 500 007, India

Published

November 1983

Manuscript received

8 November 1982