IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Loss distributions, with and without risk sharing
Claim amounts are modelled by a Pareto distribution with known α = 3 and unknown λ, where E[X] = λ/(α−1). A sample of 8 claims has a mean of ₹12,000. What is the method of moments estimate of λ?
For a Pareto with α = 3, the mean is λ/2. Equating this to the sample mean of ₹12,000 gives λ = ₹24,000. Dividing by two instead of multiplying, or multiplying by α, gives the wrong values.
- A₹4,000
- B₹6,000
- C₹36,000
- D₹18,000
- ₹24,000Correct
Explanation
E[X] = λ/(3−1) = λ/2. Setting λ/2 = 12,000 gives λ = 24,000. The option 36,000 wrongly uses a multiplier of α, and 6,000 wrongly divides the mean by 2.
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