A Goodness of Fit Test for Testing Spherical Symmetry of a Bivariate Distribution

Al-Shiha (2007) has proposed a simple test for testing spherical symmetry of a bivariate distribution. Even though, this test is powerful for some cases, it has a low power for rejecting the hypothesis of spherical symmetry for non spherically symmetric distributions that have an equal probability in each of the four quadrants. In this paper, we propose a simple test that avoids the deficiency of the test of Al-Shiha (2007). The proposed test is based on a goodness-of-fit chi-square test. The sampling distribution of the proposed test statistic follows approximately a chi-square distribution. We conduct a simulation study to evaluate the performance of the proposed test for testing spherical symmetry of a continuous bivariate distribution with known mean