IAI CS2 study guide
IAI CS2 · Work through your exam, one topic at a time.
CS2, Actuarial Statistics, is one of the technical subjects in the Institute of Actuaries of India's actuarial examination pathway. It sits alongside the modelling and economics subjects and is normally attempted after the core mathematics and probability material, because it assumes fluency with distributions, likelihood, and matrix algebra. The IAI CS2 study guide has 6 sections and about 1,668 words.
01Survival models and lifetime distributions
CS2 tests whether you can move between the survival function, density, hazard and cumulative hazard, and choose a lifetime distribution that matches a hazard shape rather than a convenient formula. For a non-negative lifetime T, S(t)=P(T t), f(t)=−S′(t), h(t)=f(t)/S(t), and H(t)=∫₀ᵗ h(u)du=−ln S(t), so S(t)=exp(−H(t)).
259 words, about 1 min02Estimation and graduation of survival models
CS2 tests nonparametric estimation from censored lifetimes and the graduation of crude rates into smooth, defensible tables. The Kaplan–Meier estimator is Ŝ(t)=∏ {t j≤t}(1−d j/n j), where d j is the number of deaths at t j and n j the risk set just before t j.
312 words, about 2 min03Regression models for survival data (Cox proportional hazards and parametric alternatives)
CS2 tests regression on survival data using Cox's semiparametric model and parametric alternatives, with emphasis on hazard ratios, partial likelihood and model checking. The Cox model assumes h(t x)=h₀(t)exp(xβ).
301 words, about 2 min04Generalised linear models
CS2 tests the GLM as a unified framework and your ability to specify the random component, link and linear predictor correctly. A GLM has independent responses from an exponential-family distribution with E(Y)=μ and Var(Y)=φV(μ), a linear predictor η=xβ, and a link g(μ)=η.
280 words, about 1 min05Bayesian statistics and computational methods
CS2 tests Bayesian inference from first principles and the computational methods needed when conjugate posteriors are unavailable. The posterior is p(θ y)∝p(θ)p(y θ).
251 words, about 1 min06Statistical modelling with R and data analysis
CS2 tests practical R skills: building model matrices, fitting survival and GLM models, extracting results and checking assumptions. Formulas use y ~ x1 + x2, with for main effects and interactions and : for interaction only.
265 words, about 1 min