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