You are given the following seriatim data on survival times for a group of 12 lives. The superscript + indicates a right-censored value.

[math]25,32^{+}, 35^{+}, 36,40^{+}, 44,48,60,62^{+}, 65,67,70^{+}[/math]

Calculate the standard deviation of the estimate of [math]S(50)[/math] using the Nelson-Aalen estimator.

• 0.1455
• 0.1519
• 0.1547
• 0.1621
• 0.1650

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Answer: A

[math]\hat{H}(50)=\frac{1}{12}+\frac{1}{9}+\frac{1}{7}+\frac{1}{6}=0.50397[/math]

[math]\hat{S}(50)=e^{-0.50397}=0.60413[/math]

[math]V[\hat{H}(50)]=\frac{11}{12^{3}}+\frac{8}{9^{3}}+\frac{6}{7^{3}}+\frac{5}{6^{3}}=0.05798[/math]

[math]V[\hat{S}(50)]=\hat{S}(50)^{2} \times V[\hat{H}(50)]=0.02116=0.1455^{2}[/math]

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.