IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Estimation procedures for lifetime distributions
Using the Nelson-Aalen estimator, the cumulative hazard just after time 6 is 0.30 and the estimated variance is based on the sum of d/n². At time 9 there are 10 at risk and 2 deaths, and the earlier variance sum is 0.0150. What is the estimated standard error of the cumulative hazard just after time 9?
The standard error is about 0.187. Add the new variance contribution d/n², which is 2/100 = 0.02, to the earlier 0.0150 to get 0.0350, then take the square root, giving roughly 0.187.
- A0.1887Correct
- B0.0356
- C0.2000
- D0.1225
- 0.1500
Explanation
Variance = 0.0150 + 2/10² = 0.0150 + 0.02 = 0.0350. Standard error = √0.0350 = 0.1871. This is closest to 0.1887? Checking: 0.1871 differs; the key 0.1887 corresponds to variance 0.0356, so data give 0.1871, nearest option is 0.1887.
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