Teste Bootstrap de normalidade univariada baseado na entropia

Abstract

The behaviour of many phenomena, in many areas of the knowledge, is described by the normal distribution of probability. When a random sample of population is taken, in the univariate case, it is common to assume that the data or residues of certain model are normally distributed. This assumption of normality must be verified through application of a statistical test. The entropy can be understood as a measure of the amount of randomness of an information system, and used to measure the uncertainty of a random variable. It is also being used for testing normality. This study is aimed to propose univariate normality tests based on entropy. These tests are computationally intensive procedures based on parametric bootstrap technique. In addition, the power of the Shapiro-Wilk normality test (TW ) was compared with the proposed univariate normality tests (T KB, T KRB 1 , T KRB 2 , T KRB C ). Computational intensive alternatives based on parametric bootstrap allowed to circumvent the limitations of sample sizes n of the existing entropy-based tests, which allow a maximum of n = 100 and also to overcome the problem of non-invariance of one of the options. The proposed tests showed adequate control of the type I error rates, if they were accurate, with sizes equal to the level of nominal significance a . Regarding performance under alternative hypotheses, at least one of the T KB, T KRB 1 , T KRB 2 , T KRB C , tests demonstrated its supremacy. Thus, we can recommend them, since they generally exceeded the concurrent best-performance test, chosen to be the reference test, the Shapiro-Wilk (TW ) test, although, still prevailing the idea of non-existence of a uniformly more powerful test for all the alternative hypotheses studied. Proposals may be used on samples over 5;000, which is one of its main virtues in relation to the test used as a reference.