Estimation of change points in a homogeneous poisson process with an application to earthquake data

This study consists of two main sections. firstly,one change point problem in a homogeneous poisson process is considered. assume that n events are observed in the continuous time interval (0,t] and the occurrence rate λ1 switches to λ2 at an unknown change point ∂(0 < t < t). our inferences are about the estimators related with the parameters t,λ1 and λ2 for the following three cases: λl,λ2 are known,λl is known,λ2 is unknown and λ1,λ2 are unknown. the estimators obtained which are based on the maximum likelihood method are investigated with a simulation study,and also are applied to the british coal mining disasters data; the results are compared with the estimations in previous studies. in the second part of the study,the situation where there are multiple change points in a homogeneous poisson process is examined. the estimations of change points are obtained for the earthquakes data set. ©2010 pakistan journal of statistics.