IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Estimation procedures for lifetime distributions
Lifetimes are exponential with rate mu. A life enters observation at age-time 3 (left truncated, having survived to 3) and is right-censored at time 8. Which is its likelihood contribution?
The contribution is exp(-5 mu). With left truncation at 3 and right censoring at 8, the contribution is S(8) divided by S(3), which equals exp(-8 mu)/exp(-3 mu). No hazard factor appears because death was not observed.
- Aexp(-8 mu)
- Bexp(-5 mu)Correct
- Cmu exp(-5 mu)
- Dmu exp(-8 mu)
- exp(-3 mu)
Explanation
Contribution is S(8)/S(3) = exp(-8mu)/exp(-3mu) = exp(-5mu). Not exp(-8mu), which ignores truncation; and no factor mu because there is no death.
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