A Cusum Test for Symmetry Against Positive Biasedness

Abstract

Let X be a random variable with an absolutely continuous distribution function F(.) and density function f(.). We propose and study a cusum test for testing the symmetry of X around zero against the one-side alternative H₁ : f( x ) ⩾ f(- x ) for all x ⩾ 0 with strict inequality for some x. The proposed test is distribution-free under the null hypothesis. The null distribution of the proposed test is given. A Monte Carlo simulation study to compare the power of the proposed test with other one-sided tests for symmetry is reported.