For i=1, … , p, let denote independent random samples from gamma distributions with unknown scale parameters θi and known shape parameters ηi. Consider testing H0:θi≤θi0 for some i=1, … , p versus H1:θi>θi0 for all i=1, … , p, where θ10, … , θp0 are fixed constants. For any 0<α<0.4, we construct two new tests that have the same size as the likelihood ratio test (LRT) and are uniformly more powerful than it. Power comparisons of our tests with other tests are given. The proposed tests are intersection–union tests. We apply the results to test the variances of normal distributions and scale parameters of two-parameter exponential distributions. Finally, we illustrate our proposed tests with an example.
Statistics:A Journal of Theoretical and Applied Statistics,