Credibility Theory and Loss Distributions

Introduction: Modeling, Random Variables, Key Functions, and Four Models and Basic Distributional Quantities. Characteristics of Actuarial Models, Creating New Distributions, Selected Distributions, and Their Relationships and The Linear Exponential Family. Frequency and Severity with Coverage Modifications. Aggregate Loss Models. Mathematical Statistics: Moments, and Percentile Estimation, Maximum Likelihood Estimation (MLE) and Bayesian Estimation. Construction of Empirical Models and Model Selection. Limited Fluctuation Credibility and Greatest Accuracy Credibility. General Applications in Credibility Theory and Loss Distributions.