IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Loss distributions, with and without risk sharing
Claims X are lognormal with parameters μ and σ². Five observed claims (₹) are e^1, e^2, e^3, e^4 and e^5. What is the MLE of σ² (using the MLE, dividing by n)?
Take logs of the claims to get 1 to 5, whose mean is 3. The sum of squared deviations is 10, and the MLE divides by n = 5, giving σ² = 2.0. Using n−1 would give 2.5.
- A2.0Correct
- B2.5
- C1.0
- D4.0
- 1.58
Explanation
Logs are 1,2,3,4,5 with mean 3. Squared deviations: 4,1,0,1,4 sum to 10. MLE divides by n=5, giving 2.0. Dividing by n−1 gives 2.5, which is the unbiased estimate and not the MLE.
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