TESTING SYMMETRY USING A TRIMMED LONGEST RUN STATISTIC

A distribution‐free test is proposed for the symmetry of a continuous distribution about a specified median. The test is based on a longest run statistic on the upper portion of the sequence of ordered ‘centred’ observations in magnitude. The probability distribution of the longest run statistic is derived, and a computationally simple and accurate approximation of the right‐tail probabilities of this statistic is given. This approximation is based on a partial fraction expansion of the corresponding generating function and is derived for use with large samples. The powers of the proposed test, some variations of the test, and other rival tests are investigated under a wide variety of asymmetric alternatives. Simulations indicate that the proposed test is competitive with other tests in terms of power performance.