Modelling the entire range of daily precipitation using phase-type distributions

Modeling the entire range of precipitation datasets using some parametric distribution is of great importance in many applications. Traditionally single-component models such as an exponential or gamma distribution have been used, but recently more flexible multi-component models have also been investigated by combining known distributions in the form of mixture or hybrid models. In this paper we introduce the phase-type (PH) distribution, a rich class of distributions previously used in other disciplines, as a parametric alternative to model the full spectrum of precipitation datasets in different areas worldwide. After discussing its distributional properties, we compare the performance of the PH model to other existing models using 49 precipitation records in Texas. The results show that the PH model performs well compared to other alternative multi-component models, in terms of likelihood-based model selection criteria and the fit in the tail part of the data. We also consider precipitation datasets of different shapes and reaffirm the ability of the PH model to capture the full spectrum of the precipitation amount. The computational complexity however remains as a possible caveat of the PH model.