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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Bhattacharya, B. Tests of Parameters of Several Gamma Distributions with Inequality Restrictions. Annals of the Institute of Statistical Mathematics 54, 565–576 (2002). https://doi.org/10.1023/A:1022411127154
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DOI: https://doi.org/10.1023/A:1022411127154