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

In a two-state alive-dead model with a constant force of mortality mu over the observation period, the likelihood for n lives is proportional to exp(-mu*V) * mu^d. What do V and d represent?

V is the total observed waiting time, the central exposed to risk, and d is the number of deaths. Each life contributes exp(-mu t) for time under observation and an extra factor mu if it dies, so the product gives exp(-mu V) mu^d.

  1. AV is the number of lives at the start and d is the number of lives at the end
  2. BV is the total waiting time (central exposed to risk) and d is the number of deaths observedCorrect
  3. CV is the initial exposed to risk and d is the number of survivors
  4. DV is the total number of deaths and d is the total time observed
  5. V is the average age at death and d is the number of lives

Explanation

Each life contributes exp(-mu*t_i) for time observed and a factor mu if death occurs. Multiplying gives exp(-mu*V) mu^d, where V is the sum of observed times (central exposure) and d is the number of deaths.

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