Statistical analysis of monthly rainfall in Central West Brazil using probability distributions
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ORIGINAL ARTICLE
Statistical analysis of monthly rainfall in Central West Brazil using probability distributions Deniz Ozonur1 · Ivana Pobocikova2 · Amaury de Souza3 Received: 3 May 2020 / Accepted: 25 August 2020 © Springer Nature Switzerland AG 2020
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. Keywords Rainfall · Probability distributions · Goodness of fit tests
Introduction Determination of a probability distribution that fits rainfall data has attracted attention in hydrology, meteorology and other fields. Investigation the best distribution representing rainfall data is one of the most popular areas in precipitation studies. It is possible to estimate the amount of precipitation quite accurately by using various probability distributions. This is very important in defining dry and wet seasons and planning water resources while making agricultural planning. * Deniz Ozonur [email protected] Ivana Pobocikova [email protected] Amaury de Souza [email protected] 1
Gazi University, Faculty of Science, Department of Statistics, Ankara 06500, Turkey
2
Department of Applied Mathematics, Faculty of Mechanical Engineering, University of Zilina, Zilina, Slovakia
3
Institute of Physics, Federal University of Mato Grosso Do Sul, Brazil, Campo Grande, MS, Brazil
There are several probability distributions that can be adjusted to the continuous random hydrologic variables. In turn, hydrological variables can be represented by more than one probability distribution. Thus, selection of appropriate probability distribution for the rainfall data is not an easy task (Al Mamoon and Rahman 2017). The most frequently used probability distributions to represent the rainfall data are generalized extreme value (GEV), Gumbel, lognormal, Pearson type III, exponential, normal, generalized logistics, Gamma, Weibull, generalized logistics, generalized Pareto, Wakeby, Kappa and Log-Pearson type III distribution
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