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Some general results about the GLR tests, for testing simple hypothesis versus two-sided hypothesis, in the family with support dependent on the parameter, are obtained. In addition, we show that such GLR tests are equivalent to the UMP tests in the same problems. Moreover, we derive the general form of the UMP tests for testing an interval hypothesis versus two-sided alternative.doi:10.19139/107 fatcat:bnaqgkceybcxro4cw5wtvngxoy