Test of Symmetry against Near Type III Positive Biasedness

One of the widely accepted assumptions in many statistical problem is that the underlying distribution is symmetric. Though a large number of nonparametric test are available in the literature for this problem, very few procedures focuses on the distributional structure when the symmetry assumption is rejected. Yanagimoto and Sibuya (1972) provided the various types of asymmetric distributional structure, positive biasedness, namely. In this paper we consider the test of symmetry against several new positive biasedness restrictions which are stronger than Yanagimoto and Sibuya's type II bias but weaker than type IV (III) bias.