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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Maximum likelihood estimators for transition intensities

An Indian insurer observes 500 lives in a two-state model with constant μ. The total waiting time is 2,000 years and there are 100 deaths. Using the asymptotic variance μ̂/V, what is the approximate 95% confidence interval for μ (using 1.96)?

The interval is 0.0402 to 0.0598. The estimate is 100/2000 = 0.05, the standard error is the square root of 0.05/2000 = 0.005, and 1.96 times this gives a margin of 0.0098 either side.

  1. A0.0402 to 0.0598Correct
  2. B0.0500 to 0.0598
  3. C0.0304 to 0.0696
  4. D0.0402 to 0.0696
  5. 0.0250 to 0.0750

Explanation

μ̂ = 100/2000 = 0.05. Variance = μ̂/V = 0.05/2000 = 0.000025, so the standard deviation is 0.005. The margin is 1.96 x 0.005 = 0.0098. The interval is 0.0402 to 0.0598. Using 500 lives as the exposure would give a wrong width.

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