A world-wide investigation of the probability distribution of daily rainfall

Daily rainfall can be modelled as an intermittent stochastic process and consequently its marginal distribution belongs to the mixed-type family of distributions, where the discrete part defines the probability dry and the rest, continuously spread over the positive real axis, determines the wet-day rainfall distribution. While the discrete part of the rainfall marginal distribution can be easily estimated, the modelling of the continuous part involves several difficulties and uncertainties, particularly in its higher tail, which is the most interesting in engineering design. A search in the literature reveals that several distributions have been used to describe the wet-day rainfall, e.g., the two-parameter Gamma, which is the prevailing model, the two- and three-parameter Log-Normal, the Generalized Logistic, the Pearson Type III, the Pareto and the Gen¬eralized Pareto, the three- and four-parameter Kappa distributions, and many more. In this study, we use daily rainfall datasets of several thousand stations, distributed over the entire globe, and we investigate the type of the distribution tail, i.e., exponential or power type, as well as its geographical variation. Two flexible probability distributions are examined, which are derived from the entropy theory (one of exponential type and the other of power type), and include as special cases most of the well-known and commonly used distributions.