G. Construction of Empirical Models 

　　1. Estimate failure time and loss distributions using   
　　a) Kaplan-Meier estimator, including approximations for large data sets
　　b) Nelson-Aalen estimator
　　c) Kernel density estimators
　　2. Estimate the variance of estimators and confidence intervals for failure time and loss distributions.
　　3. Estimate failure time and loss distributions with the Cox proportional hazards model and other basic models with covariates.
　　4. Apply the following concepts in estimating failure time and loss distribution    
　　a) Unbiasedness
　　b) Consistency
　　c) Mean squared error

　　H. Construction and Selection of Parametric Models

　　1. Estimate the parameters of failure time and loss distributions using
　　a) Maximum likelihood
　　b) Method of moments
　　c) Percentile matching
　　d) Bayesian procedures
　　2. Estimate the parameters of failure time and loss distributions with censored and/or truncated data using maximum likelihood.
　　3. Estimate the variance of estimators and the confidence intervals for the parameters and functions of parameters of failure time and loss distributions.
　　4. Apply the following concepts in estimating failure time and loss distributions
　　a) Unbiasedness
　　b) Asymptotic unbiasedness
　　c) Consistency
　　d) Mean squared error
　　e) Uniform minimum variance
　　5. Determine the acceptability of a fitted model using 
　　a) Graphical procedures
　　b) Kolmogorov-Smirnov test
　　c) Anderson-Darling test
　　d) Chi-square goodness-of-fit test
　　e) Likelihood ratio test

　　I. Credibility 

　　1. Apply limited fluctuation (classical) credibility including criteria for both full and partial credibility.
　　2. Perform Bayesian analysis using both discrete and continuous models.
　　3. Apply Bühlmann and Bühlmann-Straub models and understand the relationship of these to the Bayesian model.
　　4. Apply conjugate priors in Bayesian analysis and in particular the Poisson-gamma model.
　　5. Apply empirical Bayesian methods in the nonparametric and semiparametric cases.

　　J. Simulation 

　　1. Simulate both discrete and continuous random variables using the inversion method.   
　　2. Estimate the number of simulations needed to obtain an estimate with a given error and a given degree of confidence.
　　3. Use simulation to determine the p-value for a hypothesis test.  
　　4. Use the bootstrap method to estimate the mean squared error of an estimator.
　　5. Apply simulation methods within the context of actuarial models.
　　6. Simulate lognormal stock prices.
　　7. Incorporate jumps in stock prices by mixing Poisson and lognormal random variables.
　　8. Use variance reduction techniques to accelerate convergence.
　　9. Use the Cholesky decomposition method for simulating correlated random variables.