An analytical problem, which arises in the statistical problem of comparing the means of two normal distributions, the variances of which -as well as their ratio- are unknown, is well known in the mathematical statistics as the Behrens-Fisher problem. One generalization of the Behrens-Fisher problem and different aspect concerning the estimation of the common mean of several independent normal distributions with different variances are considered and one solution is proposed.
CitacióNikulin, M. S.; Voinov, V. G. (Vasilii Grigo'evich). "On the problem of the means of weighted normal populations". Qüestiió. 1995, vol. 19, núm. 1-3