EXACT CREDIBILITY FOR WEIGHTED OBSERVATIONS

摘要: This note generalizes Jewell's theorem on exact credibility from the classical B/Jhlmann model to (weighted) Bfihlmann-Straub model. A well-known of Jewell (1974) states that credibility, which is concurring Bayesian estimator (posterior mean) with a contract mean, found for class examples includes many common situations. In nutshell, obtains when observations are drawn frorn distributions in exponential family, natural conjugate prior risk parameter. Surprisingly, pertains only Bfihlmann model, and does not hold case different variances allowed, as BfihlmannStraub this contribution we prove well, thus allowing be averages varying numbers observations, also Poisson Binomial distributions. The parametrization used coincides one theory Generalized Linear Models. original form theorem, ours rather cumbersome reparametrizations required ordinary like Gamma special cases theorem. remedied Gerber (1995) by choosing more convenient parametrization.