Abstract: Firstly, the errors were assumed to be uniformly dependent in normal-normal cases and the Bayes premiums were derived in this model which show that it is the exact credibility. Secondly, the Bühlmann’s credibility models with uniform dependence were built, and the corresponding credibility estimators were derived. In addition, the models were extended to Bühlmann-Straub credibility in which the natural weights among contracts were introduced. However, the credibility estimators of individual premium under Bühlmann-Straub model have only the generalized form of "credibility".

Key words: error uniform dependent, orthogonal projection, credibility estimator, credibility premium, error uniform dependent, orthogonal projection, credibility estimator