Introduction to Credibility Theory

A₁ actuary aggregate claim amount approach to credibility assumed B₁ B₂ balls Bayes Bayesian approach Bayesian estimate Bayesian paradigm Bernoulli trials beta distribution binomial distribution Bühlmann credibility estimate Bühlmann estimate Bühlmann's approach Calculate the expected Chapter combination of risk conditional expectation conjugate prior Credibility Approach credibility factor denote die-spinner discrete random variable distribution with mean distribution with parameter E[X₁ error loss function expected number expected value exponential family Figure frequentist full credibility gamma distribution hypothetical means limited fluctuation approach linear approximation marked face minimum number number of claims obtain P[A₁ P[U₁ partial credibility period of observation Poisson distribution posterior distribution predictive distribution prior distribution prior probability probability density function probability distribution Proof pure premium estimates random variable representing range parameter required for full result risk characteristics Section severity distribution shooter spinner squared error loss statistical Table target U₁ unmarked faces Var(S X₁ X₁=k