Goodness-of-fit graphical assessment for a broad family of unimodal distributions

Abstract

A Skewed Exponential Power Distribution is used to construct a bidimensional array of graphics in which kurtosis varies when moving horizontally and skewness when moving vertically. The Normal distribution lies in the center of the mosaic. Given a sample, the null hypotheses that it comes from each distribution in the mosaic are tested and the cell of each distribution is filled with a color that is a function of the obtained p-value. In this way, a dark area is obtained on the mosaic to indicate the distributions with which the sample is compatible.