LIKELIHOOD RATIO TESTS FOR SYMMETRY AGAINST ONE-SIDED ALTERNATIVES

A random variable X is said to have a symmetric distribution (about 0) if and only if X and -X are identically distributed. By considering v arious types of partial orderings between the distributions of X and - X, one obtains various notions of skewness or one-sided bias. In this paper we study likelihood ratio tests for testing the symmetry of a di screte distribution about zero against the alternatives, (i) X is stoc hastically greater than -X; and (ii) pr(X = j) greater than or equal t o pr(X = -j) for all j > 0. In the process, we obtain maximum likeliho od estimators of the distribution function under the above alternative s. The asymptotic null distributions of the test statistics have been obtained and are of the chi-bar square type. A simulation study was pe rformed to compare the powers of these tests with other tests.