A Poisson-Gamma Model for Zero Inflated Rainfall Data

Abstract

Rainfall modeling is signifcant for prediction and forecasting purposes in agriculture, weather derivatives, hydrology, and risk and disaster preparedness. Normally two models are used to model the rainfall process as a chain dependent process representing the occurrence and intensity of rainfall. Such two models help in understanding the physical features and dynamics of rainfall process. However rainfall data is zero infated and exhibits overdispersion which is always underestimated by such models. In this study we have modeled the two processes simultaneously as a compound Poisson process. Te rainfall events are modeled as a Poisson process while the intensity of each rainfall event is Gamma distributed. We minimize overdispersion by introducing the dispersion parameter in the model implemented through Tweedie distributions. Simulated rainfall data from the model shows a resemblance of the actual rainfall data in terms of seasonal variation, means, variance, and magnitude. Te model also provides mechanisms for small but important properties of the rainfall process. Te model developed can be used in forecasting and predicting rainfall amounts and occurrences which is important in weather derivatives, agriculture, hydrology, and prediction of drought and food occurrences.