Random Effects Linear Statistical Models and Buhlmann-Straub Credibility

The definition and application of random effects linear models as a better alternative to empirical Bayesian credibility will be presented. A short review of Buhlmann-Straub credibility is contained in section 2. The author presents tractable formulas for quantifying the variability of credibility estimates. The variability of credibility estimates is produced without having to make distribution assumptions. However, if one assumes normality, hypothesis tests and confidence intervals can be constructed.