IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Transition intensities dependent on age (exact or census)
In a mortality investigation for ages 60 to 61, 400 lives were observed. The total time observed was 372 years, and 12 deaths occurred. Assuming a constant force of mortality over the year of age, the maximum likelihood estimate of the force of mortality is closest to:
The estimate is 12 deaths divided by 372 years of central exposure, which equals about 0.0323. Dividing by the 400 starting lives would wrongly use initial exposure and give 0.03, which does not measure time at risk.
- A0.0300
- B0.0323Correct
- C0.0333
- D0.0312
- 0.0290
Explanation
The MLE of a constant force is deaths divided by central exposed to risk: 12/372 = 0.03226, about 0.0323. Using 400 lives gives 12/400 = 0.03, which is the initial exposure mistake.
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