Tests of ordered hypotheses for gamma scale parameters. (English) Zbl 0821.62010
Summary: Three distinct alternative hypotheses: \(\theta_ i > 1\), \(i = 1,2, \dots, m\); \(\theta_ i > \theta_ 1\), \(i = 2,3, \dots, m\); and \(\theta_ 1 < \theta_ 2 < \cdots < \theta_ m\) are considered for scale parameters \(\theta_ 1, \dots, \theta_ m\) of \(m\) independent gamma families with known shape parameters. The null hypotheses are the complements of their respective alternatives. A general result concerning the likelihood ratio test (LRT) is proved and used to derive the LRT for these three hypotheses. A test more powerful than the LRT is also derived in the first case.
Keywords:
likelihood ratio test; ordered hypotheses; scale parameters; independent gamma families; known shape parametersReferences:
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