Abstract: In this Paper, the parameters and random effect of Buhlmann-Straub credibility model were researched.Two-stage estimate was used to estimate the parameter and F-test was used to test the random effect.In two-stage estimate, used orthogonal transformation to estimate aggregate average and fitting constants method to estimate variance which was unbiased.Used regression sum of squares to get the F-test statistic in order to test the random effect, the power of the test is increasing function of the test variance. AT last, the methods were used in a example that get good result.

Key words: orthogonal transformation, fitting constants method, test variance, Buhlmann-Straub model, orthogonal transformation, fitting constants method, test variance