Statistical analysis of monthly rainfall in Central West Brazil using probability distributions

Abstract

In this study, eight probability distributions such as two-parameter Weibull, three-parameter Weibull, two-parameter Rayleigh, two-parameter Gamma, three-parameter Gamma, two-parameter Lognormal, three-parameter lognormal and maximum Gumbel were applied for modelling the monthly rainfall data of the pluviometric station of Campo Grande, MS, Brazil, during the period from 1975 to 2013. The rainfall data were obtained from National Water Agency (ANA) ( https://www.ana.gov.br ). Parameters of these distributions were estimated using the maximum likelihood estimation method. Six goodness of fit tools such as chi-squared test, Kolmogorov–Smirnov test, Akaike information criterion, Bayesian information criterion, root mean square error and coefficient of determination were used to identify the best fitted probability distribution. The goodness of fit tools indicated that although no distribution provides the best fit to the rainfall data for all months, the three-parameter lognormal distribution shows generally better fit than the other distributions. The two-parameter lognormal distribution has the worst fit among the distributions.