CS1 – Actuarial Statistics
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IFoA (Institute and Faculty of Actuaries) の学習者向けの無料CS1 – Actuarial Statistics学習ノート。各章のリンクから、要点・例題・練習問題への導線にアクセスできます。
Random variables and distributions
Understand the characteristics of basic univariate distributions and how to generate samples from them
Determine the characteristics of jointly distributed random variables
Evaluate expectations and conditional expectations
Evaluate and apply generating functions
State and apply the central limit theorem
Describe random sampling and the sampling distributions of statistics commonly used in statistical inference
Statistical inference
Regression theory and applications
Bayesian statistics
Use of Bayes' theorem to calculate simple conditional probabilities
Prior distribution, posterior distribution and conjugate prior distribution
Posterior distribution for a parameter in simple cases
Use of simple loss functions to derive Bayesian estimates of parameters
Credible intervals in simple cases
Credibility premium formula and the role played by the credibility factor
Bayesian approach to credibility theory and its use for calculating credibility premiums in simple cases
Empirical Bayes approach to credibility theory and its use for deriving credibility premiums in simple cases
Understanding the differences between the Bayes and Empirical Bayes approaches and the assumptions underlying each of them
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