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Conditional tests on the scale parameter of the gamma distribution with an unknown nuisance shape parameter are considered. Such tests, based upon the conditional distribution of the sample mean x (or equivalently Wi , = x/x) given the geometric mean x, are uniformly most powerful unbiased tests. Percentage points of the conditional distribution are tabulated for small sample sizes and an asymptotic normal approximation is also obtained.
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Engelhardt et al. (1977) studied this question.
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