More Powerful Tests For Simple-Order Testing Problem With Scale Paremeters In Gamma Distributions

• Activity Number: 522 - Contributed Poster Presentations: Section on Physical and Engineering Sciences
• Type: Contributed
• Date/Time: Wednesday, August 2, 2017 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Huimei Liu* and Roger Berger and Chia-Hao Chan
• Companies: National Chengchi University and Arizona State University and
• Keywords: Intersection-union test ; likelihood ratio test ; simple order ; two-parameter exponential distribution ; uniformly more powerful test

Abstract

Let X_ij be an independent gamma random variable with known shape parameter t_i^0 and unknown scale parameter ?_i for i=1,.,p and j=1,.,n_i. Consider the simple-order testing problem of testing H_0: ?_i =?_(i+1) for "some" i=1,.,p versus ?H_1: ??_1<··· ?<??_p. For any 0<a<0.4, we construct a new test that has the same size as the likelihood ratio test (LRT) and is uniformly more powerful than the LRT. To our knowledge, this is the first a uniformly more powerful test described for these problems. The proposed test is an intersection-union test (IUT). We apply the results to test the scale parameters of two-parameter exponential distributions and the normal variances. Finally, we illustrate our proposed test with an example.