Estudo dos erros tipos I e II para testes de aderência utilizando séries sintéticas

Abstract

This paper intends to study the sensibility of two goodness of fit tests – Kolmogorov-Smirnov and Chi-Square – when a set of data is compared with a certain probability distribution. The sensibility for these tests was analyzed using Type I and Type II errors. Several synthetic series with a large number of values, generated by a known distribution (Gamma), were used. These series were submitted to the tests, which assessed the fitting of the data with four distributions: Gamma, Gumbel, Lognormal and Normal. Also, the sensibility analysis considered the variability of the data, represented by the coefficient of variation. In the end, it was found that Kolmogorov-Smirnov test shows higher Type II errors (acceptance of the false distribution) than the Chi-Square test for all the coefficients of variation. But, Kolmogorov-Smirnov test shows zero Type I errors (rejection of the true distribution). It means that this test always “recognizes” the set’s real distribution. It was observed that the series’ number of values greatly influences on the tests’ sensibility. Depending on the coefficient of variation, the rejection of a false distribution, for both tests, occurs only for very large series. In other cases, none of the tests is able to reject the false distribution.