Goodness-of-Fit Tests for the Bivariate Skew-Normal Distribution Based on a new Characterization

Abstract

In this article, we propose test statistics to test the conformity of bivariate data to the bivariate skew-normal distribution (BSN). The tests are based on partial functional mean characterization. We will use this characterization to introduce two tests, defined as the integrated deviation (ID) or integrated squared deviation (ISD) between the sample and the population partial functional means. The performance of the two tests is compared to that of the Meintanis and Hlávka (MH) and Balakrishnan et al. (BCS) tests. Using a bootstrap procedure, the proposed tests, as well as MH and BCS tests, were applied to real data. It turned out that the computational forms of the proposed tests are much simpler than that of the MH test. However, depending on the BSN shape parameters and the alternative model chosen, the proposed tests either outperform MH or the MH test outperforms the proposed tests. Except for a few cases, the proposed tests and the MH test outperform the BCS test.