Testing for symmetry and independence in a bivariate exponential distribution

Several bivariate exponential distributions have been proposed in the literature. A common problem for independent exponentials is to test the quality of the two distributions. The analogous problem for bivariate exponentials is to test for symmetry. For the bivariate exponential model of Freund (1961, Journal of the American Statistical Association 56, 971-977), tests of symmetry and independence are derived and the small sample distributions of the test statistics are found. The power function of the tests are calculated. The efficiency of the tests is found to be high on both an asymptotic and small sample basis.