Goodness of fit test for a skewed generalized normal distribution

The skewed generalized normal (SGN) distribution with four parameters is a versatile distribution that can effectively model data with skewness and heavy or light tails. In this paper, we conduct two classes of goodness of fit tests for the SGN distribution based on the empirical distribution function (edf) and the sample correlation coefficient. The first class involves transforming the sample into approximately mixed gamma observations, and then applying five classical parametric bootstrap edf-based goodness of fit tests. The second class is based on the inverse probability transformation and utilizes the sample correlation coefficient as the test statistic. We compare the finite sample performances of the proposed tests for different sample sizes and alternative distributions by extensive numerical studies. The simulation results demonstrate that the proposed tests provide a valid alternative to the standard tests using the original data, and the analysis of real data illustrates its application.