Saddlepoint approximations to exact tests and improved likelihood ratio tests for the gamma distribution

Abstract

For the most common one-sample and two-sample tests in the gamma distribution we derive the log likelihood ratio tests and the improved versions obtained by a Bartlett adjustment. For most of these tests an exact test exists and we give the saddlepoint approximation to the latter. The tests are compared with previously published tests and a small simulation study is included.

Keywords:

• asymptotic expansion
• bartlett correction
• conditional test