Mosaic normality test

Abstract

A procedure is proposed here for jointly visualizing the compatibility of a sample with a family of Skewed Exponential Power Distributions, of which the distributions known as Normal, Exponential, Laplace and Uniform are particular cases. The procedure involves constructing a mosaic that contains these distributions in such a way that the asymmetry varies from left to right and the kurtosis varies from top to bottom. The null hypothesis that the sample belongs to each of the mosaic distributions is tested, with the corresponding box for each distribution being shaded in a gray scale according to the p-value obtained. The location and shape of the shaded area that appears on the mosaic facilitates not only identifying which distributions are compatible with the sample, but also assessing the power of the test performed. All the parameters that define the distribution are considered to be known. The problem remains open for expanding the procedure to cases in which these parameters are not known but must be estimated from the sample. As additional material, a code written in R that carries out the proposed test is included.

Keywords:

• Normality tests
• goodness-of-fit methods
• power test
• graphical methods