Mixture models of probability distributions applied to rainfall in the state of Pernambuco, Brazil

The Brazilian semi-arid region is recurrently affected by the scarcity of water that marks the landscape as it prints periods of severe drought. Therefore, rainfall in this region greatly influences plant growth in regional hydrological processes that affect droughts or floods. It is of practical interest to assess how changes in rainfall patterns occur to anticipate hydrological dynamics. However, this is not easy as climate change reshapes global hydrology. Thus, assertive forecasting has become rare and imputed estimates of a reasonable degree of uncertainty. The objective of this work was to verify from the mixture of exponential, gamma, beta, log-normal, Weibull, normal, log-logistic, and exponentiated log-logistic distributions, which best fits the monthly rainfall of the state of Pernambuco, Brazil. The data used came from 133 monthly rainfall series (1950 to 2012) distributed over the state of Pernambuco. The Maximum Likelihood Method estimated all parameters. The Kolmogorov-Smirnov adherence test was applied at 5% probability to assess the adjustments. The least rejected distributions in the adherence test were Weibull, gamma, and beta; October presented the smallest number of distributions considered adequate to model monthly rainfall. More than 99% of the rain gauge stations had some adequate probabilistic distribution to model monthly rainfall in March. For most months, except for March, the Weibull distribution was the most suitable for modeling the monthly rainfall in the vast majority of rain gauge stations of Pernambuco.