Exam MAS-I: Modern Actuarial Statistics I Study Guide
Probability, statistics, regression, time series, Bayesian analysis, and simulation for CAS candidates.
Overview
Exam MAS-I (Modern Actuarial Statistics I) covers probability, mathematical statistics, regression, time series, and Bayesian methods for CAS candidates. It emphasizes both theoretical understanding and the ability to apply statistical methods to insurance data. The exam replaced the former Exam S and Exam 3L statistical content.
Exam Format
- Duration
- 240 minutes (4 hours)
- Questions
- 40 multiple-choice questions
- Pathway
- CAS
- Format
- Computer-based testing (CBT)
Topic Breakdown
Probability
15-20%Distributions, moment-generating functions, transformations, order statistics, multivariate distributions
Mathematical Statistics
20-25%Point estimation (MLE, method of moments), confidence intervals, hypothesis testing, sufficiency
Regression
15-20%Multiple linear regression, diagnostics, variable selection, weighted least squares, GLMs
Time Series
10-15%Stationary processes, AR, MA, ARMA, ARIMA models, forecasting, spectral analysis
Bayesian Analysis
15-20%Prior and posterior distributions, conjugate priors, credible intervals, predictive distributions
Simulation
5-10%Inverse transform, acceptance-rejection, variance reduction (antithetic, control variates, stratified sampling)
Recommended Study Approach
- 1
Review core probability distributions and their properties, including moment-generating functions and transformations.
- 2
Master maximum likelihood estimation, including setting up likelihood functions and solving score equations.
- 3
Study hypothesis testing with a focus on likelihood ratio tests, chi-squared tests, and p-value interpretation.
- 4
Practice regression problems involving diagnostics, influential observations, and model comparison.
- 5
For Bayesian analysis, work through conjugate prior problems (Beta-Binomial, Gamma-Poisson, Normal-Normal) repeatedly.
- 6
Learn simulation techniques including inverse transform, acceptance-rejection, and variance reduction methods.
Related Topics
Statistics and Data Analysis
Descriptive statistics, hypothesis testing, confidence intervals, and data visualization.
Regression and Predictive Modeling
Linear and logistic regression, GLMs, model selection, and predictive analytics.
Time Series Analysis
AR, MA, ARIMA models, forecasting, stationarity, and seasonal decomposition.
Credibility Theory
Buhlmann, Buhlmann-Straub, classical credibility, and empirical Bayes methods.
Survival Analysis
Kaplan-Meier estimation, Cox regression, hazard functions, and censoring.
Bayesian Statistics
Prior and posterior distributions, conjugate families, MCMC, and Bayesian estimation.
Machine Learning for Actuaries
Decision trees, random forests, gradient boosting, neural networks, and clustering.
Stochastic Processes
Markov chains, Poisson processes, Brownian motion, and their actuarial applications.
Cheat Sheets
Probability Distributions Cheat Sheet
Quick reference for all probability distributions tested on actuarial exams, including PMFs, PDFs, means, variances, and MGFs.
Statistics and Regression Cheat Sheet
Key formulas for regression analysis, hypothesis testing, and model diagnostics.
Credibility Theory Cheat Sheet
Buhlmann, Buhlmann-Straub, classical credibility, and empirical Bayes formulas.