Testing the equality of several gamma means: a parametric bootstrap method with applications

Abstract

We apply a recently developed ‘Computational Approach Test’ (CAT), a variant of the parametric bootstrap method, to test the equality of means of several gamma distributions. All parameters are assumed to be unknown, and we consider two cases-(i) the shape parameters, though unknown, are assumed to be equal; and (ii) the shape parameters are all unknown and possibly unequal. The CAT, as applied to the above two cases, doesn’t require the knowledge of any sampling distribution, depends heavily on numerical computations and Monte-Carlo simulation, and figures out the critical region automatically. The power and/or size of our proposed CAT is quite encouraging compared with the other tests reported in the literature. The proposed method can be used as a logical alternative approach to classical one-way ANOVA when one is not sure about normality, and positively skewed distribution is a possibility for the observed data. Though the proposed CAT has been used recently to compare normal means by the present authors, its usefulness for comparing gamma means hadn’t been studied before. This paper shows that the CAT can be as good as, if not better than, the other proposed methods discussed in the literature to test the equality of several gamma means. Real life datasets have been used to illustrate the applicability of this method. Also, our comprehensive numerical study reveals that some of the frequently cited methods are not as good as they are claimed to be.