Tests for gamma distribution based on its independence property

Abstract

There are two test statistics proposed in this study in order to test whether data come from a gamma distribution. Both of the proposed test statistics are developed from a modified Kendall coefficient based on the independence property of a gamma distribution. The first one is asymptotically distributed as standard normal and the limit distribution function of the second one was improved using an Edgeworth expansion and the Jackknife method. They are invariant to scale parameters and perform substantially better than existing tests in terms of Type I error rate and test power, especially in cases with samples of moderate size.