Statistical normality and homogeneity of a 71-year rainfall dataset for the state of Rio de Janeiro-Brazil

Studies are scarce on the application of normality and homogeneity tests for rainfall series in the state of Rio de Janeiro, Brazil. Therefore, this study applies normality and homogeneity tests in a 71-year time series (1943-2013) of rainfall, seeking to identify which tests were most indicated in the evaluation of the normality and homogeneity of rainfall data in Rio de Janeiro. The tests of normality and homogeneity of variance were divided into (i) parametric-Shapiro-Wilk (SW) and Jarque-Bera (JB)-and (ii) non-parametric-Bartlett (B) and Fligner-Killeen (FK). All statistical procedures were performed using the open software R version 3.4.2. The tests of normality (SW and JB) and homogeneity of variance (B and FK) applied to the raw (unfilled) data showed that both the SW and JB tests were not satisfactory in determining the normality of the series, with only two stations reaching over 95% reliability. Regarding the homogeneity of variance of the standardized residues in the raw data, the B test stands out when compared to the FK test. After completing data faults of the data, the SW, JB, B, and FK tests pointed to rejection of the normality and homogeneity hypotheses for the specific time series. According to the adopted methodology, there are 15 useful stations (65.22%), 7 dubious (30.43%), and one suspicious (4.35%). The SW and B tests presented better results when matched to the other tests. The proposed methodology should be considered for further investigation of normality and homogeneity in other climate datasets.