TESTS OF PARAMETERS OF SEVERAL GAMMA DISTRIBUTIONS WITH INEQUALITY RESTRICTIONS

BHASKAR BHATTACHARYA

Department of Mathematics, Southern Illinois University, Carbondale, IL 62901-4408, U.S.A.

(Received June 29, 2000; revised April 9, 2001)

Abstract. Gamma distribution is one of the most used methods of modeling lifetime data. However, testing homogeneity of parameters of m ≥ 3 gamma distributions against order restrictions is almost non-existent in the current literature. We propose two methods to this end: one uses quadratic forms involving ratios of cumulants as test statistic and the other is a stepwise procedure which uses Fisher’s method of combining p-values when shape parameters are equal but unknown. Both procedures allow use of arbitrary sample sizes of m populations. Test of the inequality restrictions as a null hypothesis against unrestricted alternatives is also considered. A Monte Carlo study of power at various alternatives shows that both methods are competitive when they are applicable.

Key words and phrases: Approximate tests, cumulants, Fisher’s combination method, Monte Carlo studies, order restricted tests, quadratic forms.