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

In a constant-force two-state model, 40 deaths are observed over 2,000 life-years of exposure. Using the asymptotic variance approximation μ̂²/d, what is an approximate 95% confidence interval for μ (use 1.96)?

The estimate is 0.02 with standard deviation about 0.0032, since the variance is μ̂²/d. Adding and subtracting roughly 1.96 standard deviations gives an interval of approximately 0.014 to 0.026, matching the first option.

  1. A0.0141 to 0.0259Correct
  2. B0.0200 to 0.0392
  3. C0.0082 to 0.0318
  4. D0.0163 to 0.0237
  5. 0.0100 to 0.0300

Explanation

μ̂ = 40/2000 = 0.02. Variance ≈ μ̂²/d = 0.0004/40 = 0.00001, so the standard deviation is 0.003162. The margin is 1.96×0.003162 = 0.0062, giving 0.0138 to 0.0262 approximately. The closest option is 0.0141 to 0.0259 (computed with a slightly rounded standard deviation of 0.003).

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