CS1 – Actuarial Statistics
7 个单元 · 44 个章节
免费 CS1 – Actuarial Statistics 学习笔记，适合 IFoA (Institute and Faculty of Actuaries) 学生。每个章节都覆盖一个重点主题，并附例题与可延伸到 thinka app 的练习提示。
Data analysis
Aims, stages and tools of a data analysis
Data sources, large data sets and reproducible research
Summary statistics and exploratory data visualisation
Correlation: Pearson, Spearman and Kendall
Principal component analysis
Random variables and distributions
Discrete distributions and their properties
Continuous distributions and their properties
The Poisson process and simulation by inverse transform
Joint distributions, independence and covariance
Conditional expectation and conditional variance
Moment and cumulant generating functions
The central limit theorem
Random sampling and sampling distributions
Statistical inference
Method of moments and maximum likelihood estimation
Properties of estimators: bias, mean square error, efficiency, consistency
Asymptotic distribution of MLEs and the bootstrap
Confidence intervals for normal, binomial and Poisson parameters
Two-sample and paired intervals; prediction intervals
Hypothesis testing concepts, errors and power
One-sample, two-sample, paired and permutation tests
Chi-square goodness of fit and contingency tables
Regression theory and applications
Simple linear regression and least squares estimation
Multiple linear regression and choice of explanatory variables
Inference on the slope, goodness of fit and prediction intervals
Residual analysis and model validation
The exponential family, variance function and scale parameter
Link functions and the linear predictor: variables, factors, interactions
Deviance, parameter estimation and model selection in GLMs
GLM residuals and tests of model acceptability
Bayesian statistics and credibility theory
Bayes' theorem and conditional probability
Prior, posterior and conjugate prior distributions
Deriving posterior distributions in simple cases
Loss functions and Bayesian estimators
Credible intervals
The credibility premium formula and the credibility factor
Bayesian credibility theory
Empirical Bayes credibility theory and its assumptions
Bayesian statistics
Understanding the differences between the Bayes and Empirical Bayes approaches and the assumptions underlying each of them
Statistical software skills (Paper B)
Simulating random variables and samples in R
Probabilities, quantiles and summary statistics in R
Exploratory plots and correlation output in R
Fitting and interpreting linear regression output
Fitting and interpreting generalised linear model output
Tests and confidence intervals using software output
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