MAS-I Statistics
The MAS-I statistics domain is the bridge from undergraduate mathematical statistics into actuarial claim frequency, severity, aggregate, censoring, truncation, and estimation work.
CAS Exam MAS-I
CAS exam page and content outline are mapped for domain weights, item types, cognitive levels, table conventions, and reading groups.
What the official PDFs establish
- Appointment length
- 4.5-hour appointment with a 4-hour exam duration.
- Scheduled break
- The appointment includes a scheduled 15-minute break plus tutorial/confidentiality/survey time.
- Item types
- Question formats include multiple choice, multiple selection, point and click, fill in the blank, and matching.
Topic and domain coverage
| Topic | Weight | Source |
|---|---|---|
| Probability Models | 20-30% | Source: MAS-I Content Outline 2025, p. 2 |
| Statistics | 20-30% | Source: MAS-I Content Outline 2025, p. 3 |
| Extended Linear Models | 45-55% | Source: MAS-I Content Outline 2025, p. 5 |
| Cognitive level: Remember | 5-10% | Source: MAS-I Content Outline 2025, p. 1 |
| Cognitive level: Understand and Apply | 55-60% | Source: MAS-I Content Outline 2025, p. 1 |
| Cognitive level: Analyze and Evaluate | 35-40% | Source: MAS-I Content Outline 2025, p. 1 |
Chapter and reading intelligence
- Official readings
The outline lists readings from Daniel, Dobson and Barnett, Hogg/McKean/Craig, James et al., Larsen, Ross, Struppeck, and Tse.
Source: MAS-I Content Outline 2025, p. 7 - Extended linear models
This is the largest content domain and should drive the first MAS-I concept cluster.
Source: MAS-I Content Outline 2025, p. 5
Official files used by the map
- CAS content outlinecontent-outline
Primary source for domain weights, item types, and readings.
Source: MAS-I Content Outline 2025
Quick Answer
The official MAS-I outline gives statistics a 20-30% weight. It names sample estimation, sufficient statistics, hypothesis tests, tests of means and variances, insurance claim frequency and severity, aggregate claims, order statistics, maximum likelihood estimation, censoring, truncation, and missing data.
This domain rewards careful setup. Most errors are not exotic theory errors; they come from choosing the wrong sample statistic, testing the wrong hypothesis, or building the wrong likelihood for censored or truncated data.
Estimation And Sufficiency
Know how to estimate a mean and variance from sample data, and know what a sufficient statistic is doing: preserving all sample information about the parameter inside the chosen model family.
For estimator comparison, separate bias, variance, mean square error, consistency, efficiency, and sufficiency. Those words are not synonyms, and MAS-I can test the distinction directly.
Hypothesis Tests
Hypothesis testing on MAS-I includes Type I and Type II errors plus tests of means and variances using critical values from sampling distributions. The exam may ask for a calculation, a rejection decision, or an interpretation of the error probabilities.
Write the null and alternative before computing. Then identify the statistic, distribution under the null, rejection region, and conclusion in context.
Type I or Type II?
An insurer rejects a pricing model even though the model's null assumption is actually true. Which error is that?
Type I error
Type I error means rejecting the null hypothesis when the null is true.
Type II error
Type II error means failing to reject the null hypothesis when the alternative is true.
Sampling variance
Sampling variance can cause errors, but it is not the name of this decision error.
MLE With Actuarial Data
Maximum likelihood estimation becomes more exam-relevant when data are incomplete. Censoring changes what was observed after a threshold or time. Truncation changes which observations enter the sample at all.
For complete observations, density terms usually enter the likelihood. For right-censored observations, survival terms enter. For truncated samples, the density must be conditioned on being observable.
Claims And Aggregates
The statistics domain explicitly includes claim frequency, claim severity, and aggregate insurance claims. That means count and severity families are not just probability review; they are the statistical inputs to actuarial aggregate models.
A good MAS-I answer names the model object: count, severity, or aggregate. Then it chooses the statistic or likelihood that matches that object.
Order Statistics
Order statistics matter because actuarial data often care about extremes, thresholds, and ranked losses. Know what the minimum, maximum, and kth order statistic represent before using formulas.
If a problem asks about the largest claim in a sample, the distribution is built from the event that all observations are below the threshold. If it asks about the kth smallest claim, the binomial count of observations below the threshold is usually nearby.
Original Practice Drill
A severity sample records exact losses below 10,000, but any loss above 10,000 is reported only as greater than 10,000. Write the likelihood contribution for the exact losses and the capped reports under a fitted severity model.
A strong solution identifies the reports above 10,000 as censored observations and uses survival terms for them. Do not treat them as exact losses equal to 10,000.