Statistical Validation of Non-Homogeneous Poisson Processes via Time-Rescaling

Abstract

Non-Homogeneous Poisson Processes (NHPPs) model events with time-varying arrival rates, making them useful across fields such as seismology, meteorology, and infrastructure risk analysis. This paper tests for NHPP behavior by estimating time-dependent intensity functions, applying the Time-Rescaling Theorem to transform event times, and using the Kolmogorov-Smirnov test to evaluate goodness of fit. Using R software, we apply this framework to real-world datasets, including tornado occurrences, earthquake events, wildfire incidents, and oil pipeline accidents, providing a practical approach to assessing the suitability of NHPPs in diverse settings.