AISM 54, 565-576
© 2002 ISM

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 $m\geq 3$ 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.

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