Probabilistic analysis of the distribution of daily rainfall in the State of Paraná

Rainfall in Brazil has a different distribution compared with northern hemisphere countries where hydrological research employs climatic data simulators developed and calibrated for Europe and/or the USA. Thus, these simulators do not produce very satisfactory results when applied to data of Brazilian weather stations. With the aim of introducing the Mixed Exponential probability distribution as an alternative to model rainfall data in Brazil, this work probabilistically analyzed the distribution of daily rainfall data in the State of Paraná, by determining which probability density functions best fit the historical monthly series. The historical series of thirty years (1980-2009) of 29 locations were used, in order to evaluate the fit of the Exponential, Gamma, Weibull, Log-Normal, Mixed Exponential and Generalized Pareto probability distributions, based on the non-parametric Anderson-Darling and Chi-Square tests. In the analyses without the Mixed Exponential distribution, the largest p-value in the two tests occurred most frequently in the Gamma distribution, followed by the Weibull distribution. When the Mixed Exponential was included in the analysis, the largest p-value occurred most frequently in the tests of adhesion, reaching 73.85% of the time in the Anderson-Darling test and 71.84% of the time in the Chi-Square test.