Predicting intensity function of nonhomogeneous Poisson process

The nonhomogeneous Poisson process is commonly utilized to model the occurrence of events over time‎. ‎The identification of nonhomogeneous Poisson process relies on the intensity function‎, ‎which can be difficult to determine‎. ‎A straightforward approach is to set the intensity function to a constant value‎, ‎resulting in a homogeneous Poisson process‎. ‎However‎, ‎it is crucial to assess the homogeneity of the intensity function through an appropriate test beforehand‎. ‎Failure to confirm homogeneity leads to an infinite-dimensional problem that cannot be comprehensively resolved‎. ‎In this study‎, ‎we analyzed data on the number of passengers using the Tehran metro‎. ‎Our homogeneity test showed a nonhomogeneous arrival rate of passengers‎, ‎prompting us to explore different functions to estimate the intensity function‎. ‎We considered four functions and used a piecewise function to determine the best intensity function‎. ‎Our findings showed significant differences between the two models‎, ‎highlighting the effectiveness of the piecewise function model in predicting the number of metro passengers.