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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Transition intensities dependent on age (exact or census)

In the two-state model, the maximum likelihood estimator of a constant force of mortality μ is based on observed data from n lives. Which is correct?

The maximum likelihood estimator is total observed deaths divided by total time lived by all lives (central exposed to risk). This follows from maximising μ^d e^(-μv). Dividing by initial numbers estimates a probability, not a rate.

  1. ATotal deaths divided by the number of lives at the start
  2. BTotal deaths divided by total waiting (exposed-to-risk) timeCorrect
  3. CTotal waiting time divided by total deaths
  4. DTotal deaths divided by the number of survivors at the end
  5. Total deaths multiplied by the average time lived

Explanation

The likelihood is proportional to μ^d e^(-μv), where d is deaths and v is total time lived. Maximising gives μ-hat = d/v. Option 0 estimates a probability, not a rate. Option 2 is the reciprocal.

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