Generalized p-value and Generalized Confidence Interval for the Behrens-Fisher Problem with Prior Information

In this paper, the generalized p-value and the new generalized confidence interval for the difference between two normal population means with prior information are investigated. Some prior knowledge of parameters, for example, are a) known ratio of variances b) one of variance is unknown and c) known coefficients of variation. In each case, we derive both generalized p-value and generalized confidence interval based on Tsui and Weeranhandi [1989, Generalized p-values in significance testing of hypotheses in the presence of nuisance parameter, J. Amer. Statistics. Assoc. 84, 602-607] andWeerahandi [1993, Generalized confidence interval, J. Amer. Statistics Assoc. 88, 899-905, 1993].