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Keywords
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Generalized likelihood ratio test, nuisance parameter, one-sided hypothesis, two-sided hypothesis,
uniform distribution, uniformly most powerful test
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Abstract
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The problem of finding optimal tests in the family of uniform distributions is investi-
gated. The general forms of the uniformly most powerful and generalized likelihood ratio tests are
derived. Moreover, the problem of finding the uniformly most powerful unbiased test for testing two-
sided hypothesis in the presence of nuisance parameter is investigated, and it is shown that such a test
is equivalent to the generalized likelihood ratio test for the same problem. The simulation study is
performed to evaluate the performance of power function of the tests.
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