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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Estimation procedures for lifetime distributions

For a group of lives aged x, the observed central exposed to risk is 2,000 person-years with 50 deaths, and the force of mortality is assumed constant over the year. The estimate of q_x is closest to:

With a constant force, the estimated force is 50 divided by 2,000, which is 0.025. The probability of death is then one minus e to the power of minus 0.025, which is about 0.0247, slightly below the force itself.

  1. A0.0250
  2. B0.0247Correct
  3. C0.0253
  4. D0.0500
  5. 0.0125

Explanation

Constant force: mu-hat = 50/2000 = 0.025. Then q_x = 1 − e^(−0.025) = 1 − 0.97531 = 0.02469, about 0.0247. Option 1 equates q with mu directly, ignoring the exponential. Option 3 would be wrongly using mu/(1−mu/2), which is not exact under a constant force.

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