## Abstract

For i=1, … , p, let (Formula presented.) denote independent random samples from gamma distributions with unknown scale parameters θ_{i} and known shape parameters η_{i}. Consider testing H_{0}:θ_{i}≤θ_{i0} for some i=1, … , p versus H_{1}:θ_{i}>θ_{i0} for all i=1, … , p, where θ_{10}, … , θ_{p0} 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.

Original language | English |
---|---|

Pages (from-to) | 564-577 |

Number of pages | 14 |

Journal | Statistics |

Volume | 49 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2015 May 4 |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty