ACAS exams & assessments

MAS-I

Modern Actuarial Statistics I

5 discussions

Study strategy

MAS-I: Keep an assumption-first error log

A calculator error and an incorrect model assumption need different repairs. For each practice mistake, record the intended random variable, assumptions, setup and numerical calculation. This makes repeated conceptual errors visible instead of hiding them in an overall score.

Worked example or practice scenario

A Poisson-model mistake could be recorded as “used annual rate on a monthly interval.” A likelihood mistake could be “treated right censoring as an event.” A GLM mistake could be “interpreted log-link coefficient as an additive response change.”

Try this next

Create a fresh example for each error and solve it after a delay. Practise the current official item types in the official testing resources. Vendor difficulty levels and forum pass estimates are not substitutes for the content outline.

Reading sources

Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1

Explanation

MAS-I: AIC comparisons require comparable likelihoods

AIC balances fitted likelihood and parameter count. It is designed for comparisons on a compatible data and likelihood basis. A smaller value is not proof of causation or assurance that a model predicts well under a different population.

Worked example or practice scenario

Models A and B fit the same response observations. A has log likelihood −120 with 3 fitted parameters, giving AIC 246. B has log likelihood −116 with 8 parameters, giving AIC 248. Better fit alone does not make B the AIC choice.

Try this next

Count parameters consistently, including estimated dispersion where applicable. Do not compare values from different response transformations without accounting for the likelihood basis. Follow model selection with diagnostics and a relevant predictive check.

Reading sources

Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1

Explanation

MAS-I: Poisson arrivals and exponential waiting times share a rate

A homogeneous Poisson process links counts in a fixed time interval with exponentially distributed waiting times. Keep rate and time units consistent. Independence and a constant rate are assumptions, not consequences of the word “arrival.”

Worked example or practice scenario

At rate 3 per hour, the probability of no arrival in 20 minutes is e^(−3/3)=e^−1. The expected first waiting time is 1/3 hour. In two hours the expected count is 6, a different random variable.

Try this next

Calculate the probability of at least one arrival and check it complements the no-arrival probability. Then describe why an arrival rate that varies by time of day requires a different specification.

Reading sources

Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1

Explanation

MAS-I: Censoring contributes a survival probability to likelihood

An observed event at time t contributes a density or probability mass appropriate to the observation. A right-censored record tells you that the event has not occurred by t; it contributes a survival probability, not a density at t.

Worked example or practice scenario

With independent exponential lifetimes, one observed event at time 2 and one right-censored record at time 5 give likelihood λe^(−2λ) × e^(−5λ)=λe^(−7λ). The MLE is 1/7. Treating the censored record as another death would incorrectly give 2/7.

Try this next

Derive the log likelihood and its derivative. Record what is observed for each subject. Consider whether censoring is independent of the event process before applying the standard likelihood construction.

Reading sources

Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1

Explanation

MAS-I: Exposure belongs in a Poisson count model

For varying observation periods, expected count is exposure times an underlying rate. In a log-link Poisson model, log exposure can enter as an offset with coefficient fixed at one. It is not a free predictor whose effect must be estimated.

Worked example or practice scenario

Two otherwise identical policies have exposures .5 and 1.0 years. If the fitted annual rate is .08, expected counts are .04 and .08. Equal counts would imply different fitted rates, not equal risk.

Try this next

Write the model on both the count and rate scales. Check that a zero exposure is not blindly sent into a logarithm. Then explain how an overdispersion diagnostic can challenge the Poisson variance assumption without changing what exposure means.

Reading sources

Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1