A Two-Sample Test of Equal Gamma Distribution Scale Parameters With Unknown Common Shape Parameter

Abstract

An approximate F-test for the equality of two gamma distribution scale parameters, given equal but unknown shape parameters, is proposed and investigated. The test is obtained by replacing the shape parameter by its maximum likelihood estimate. Monte Carlo and asymptotic results show that in many cases this substitution does not seriously affect the nominal test size. Additionally, these results can be used to modify the test to more closely achieve the desired size. An example from a cloud seeding experiment is given.

KEY WORDS:

• Gamma distribution
• Two-sample tests
• Tests of equal scale parameters
• Approximate tests
• Maximum likelihood