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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 model with constant force of mortality mu, which statement about the exact waiting time T until death for a life aged x is correct?

With constant force of mortality mu, the future lifetime is exponentially distributed with mean 1/mu, because the survival function is exp(-mu t). Hazards that vary with age give Gompertz or Weibull forms instead.

  1. AT is exponentially distributed with mean 1/muCorrect
  2. BT is uniformly distributed over (0, 1/mu)
  3. CT has a Gompertz distribution with mean mu
  4. DT is exponentially distributed with mean mu
  5. T has a Weibull distribution with increasing hazard

Explanation

A constant hazard gives t p_x = exp(-mu t), the exponential survival function, with mean 1/mu. Mean mu would be dimensionally wrong. Gompertz and Weibull (shape above 1) have age-dependent hazards.

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