An Exact and Near-Exact Distribution Approach to the Behrens–Fisher Problem

The Behrens–Fisher problem occurs when testing the equality of means two normal distributions without assumption that variances are equal. This paper presents approaches based on exact and near-exact for test statistic problem, depending different combinations even or odd sample sizes. We present distribution both sizes one even. a finite mixture generalized integer gamma (GIG) distributions, used as an approximation to distribution, which consists infinite series. proposed tests, compared with Welch’s t-test through Monte Carlo simulations, in particular small unbalanced results show competent solutions exhibiting precise better powers than approach those cases. Numerical studies tends be bit more conservative statistics unbalanced, situations obtain higher t-test.