CS1 —Actuarial Statistics

CS1 provides a grounding in the statistical and mathematical techniques used to analyse data, estimate parameters, and draw defensible conclusions from uncertain information — the toolkit every later actuarial subject assumes you already have.

Under the pre-2019 exam structure, CS1 combined two separate papers: CT3 (Probability and Mathematical Statistics) and the Bayesian/credibility portion of CT6 (Statistical Methods). The first thirteen chapters build the general statistics toolkit (old CT3 territory), while the final three chapters — Bayesian statistics and credibility theory — carry over the CT6 material on blending individual and portfolio-level experience.

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Chapter List — CT3 vs CT6

CT3 (Probability and Mathematical Statistics)
  • 1. Data analysis
  • 2. Probability distributions
  • 3. Generating functions
  • 4. Joint distributions
  • 5. Conditional expectation
  • 6. Central Limit Theorem
  • 7. Sampling and statistical inference
  • 8. Point estimation
  • 9. Confidence intervals
  • 10. Hypothesis testing
  • 11. Correlation
  • 12. Linear regression
  • 13. Generalised linear models
CT6 (Statistical Methods — Bayesian and Credibility)
  • 14. Bayesian statistics
  • 15. Credibility theory
  • 16. Empirical Bayes credibility theory

PART 1 : — Foundations of Data and Distributions (Chapters 1–4)

Every statistical model starts with data and a distribution to describe it. Data analysis covers how to explore, clean, and summarise a raw data set — the unglamorous but essential first step of any actuarial project. Probability distributions then builds the library of models actuaries reuse constantly: the Poisson distribution for claim counts, the lognormal or Pareto distribution for claim severity, and so on. Generating functions give you an algebraic shortcut for combining random variables — for instance, working out the total claims distribution for a whole portfolio without having to convolve distributions directly. Joint distributions extends this to situations where two or more risks move together, such as a couple’s joint mortality in a pension scheme, or correlated claim types within a single policy.

PART 2 : — Inference from Samples (Chapters 5–10)

This block is about drawing reliable conclusions from limited data. Conditional expectation and the Central Limit Theorem provide the theoretical backbone — the CLT, in particular, is why insurers can rely on average claim experience being predictable once a portfolio is large enough, even when individual claims are wildly uncertain. Sampling and statistical inference, point estimation, and confidence intervals then teach you how to estimate an unknown quantity (like a mortality rate or a claim frequency) from sample data, and how confident you can be in that estimate. Hypothesis testing rounds this off — the exact technique used to test, say, whether a new underwriting question actually reduces claims, or whether a change in claims process has genuinely shifted average payout sizes.

PART 3 : — Relationships and Modern Pricing Models (Chapters 11–13)

Correlation and linear regression teach you how to quantify and model the relationship between variables — for example, how claim frequency changes with a policyholder’s age, or how claims costs trend with medical inflation over time. Generalised linear models (GLMs) then generalise this into the workhorse technique behind modern insurance pricing: GLMs are what sit behind most motor and health insurance rating engines in India today, translating dozens of rating factors (age, vehicle type, location, claims history) into a single technical premium.

PART 4 : — Bayesian and Credibility Methods (Chapters 14–16)

This final block addresses a very practical actuarial problem: how much should you trust a small insured group’s own claims history versus the wider portfolio’s experience? Bayesian statistics gives you a formal way to update a prior belief (say, the industry-average claim rate) using new evidence (a specific client’s actual claims). Credibility theory and empirical Bayes credibility theory turn this into a workable formula — a “credibility factor” that blends individual and group experience — which is exactly how insurers set renewal premiums for a large corporate group health scheme, or calibrate a No-Claim Bonus system, without over-reacting to a small sample of good or bad luck.

Exam Format

Both papers are computer-based. Paper A is a 3¼-hour computer-based exam covering a range of questions of varying marks. Paper B is a 1¾-hour computer-based practical exam using R, covering data analysis and statistical modelling problems. Both papers must be sat in the same exam sitting, with a combined mark determining the pass.

Prerequisites

No prior actuarial exams are required. CS1 is typically one of the first Core Principles subjects students attempt.