Tests of Parameters of Several Gamma Distributions with Inequality Restrictions |
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Authors: | Bhaskar Bhattacharya |
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Affiliation: | (1) Department of Mathematics, Southern Illinois University, Carbondale, IL, 62901-4408, U.S.A |
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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. |
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Keywords: | Approximate tests cumulants Fisher's combination method Monte Carlo studies order restricted tests quadratic forms |
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