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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Loss distributions, with and without risk sharing

Claim sizes are gamma with parameters α and λ. A sample has mean ₹800 and variance 320,000 (₹²). Using method of moments, what is the estimate of α?

For a gamma, mean = α/λ and variance = α/λ². The ratio 320,000/800 = 400 gives λ = 0.0025, so α = 800 × 0.0025 = 2.0. Squaring the mean over the variance gives the same result.

  1. A0.50Correct
  2. B2.00
  3. C0.25
  4. D1.25
  5. 0.80

Explanation

Mean = α/λ, variance = α/λ². So variance/mean = 1/λ = 400, giving λ = 0.0025. Then α = mean × λ = 800 × 0.0025 = 2.0. Option 0.50 results from inverting the ratio.

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