Actuarial Outpost
 
Go Back   Actuarial Outpost > Exams - Please Limit Discussion to Exam-Related Topics > SoA/CAS Preliminary Exams > Exam 4/C - Construction and Evaluation of Actuarial Models
FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

Salary Surveys
Property & Casualty, Life, Health & Pension

Health Actuary Jobs
Insurance & Consulting jobs for Students, Associates & Fellows

Actuarial Recruitment
Visit DW Simpson's website for more info.
www.dwsimpson.com/about

Casualty Jobs
Property & Casualty jobs for Students, Associates & Fellows


Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 06-11-2011, 11:55 AM
Fiip27 Fiip27 is offline
 
Join Date: May 2010
Posts: 4
Default TIA Review Problem 235

How do they calculate the Nelson-Aalen estime of H(X), used with the survival function, for Jack to be 1/3 and Jill to be 1/3 + 1/4?

I'm interpreting this problem as 5 regular observations, plus 2 censored observations at 25 and 35.
Reply With Quote
  #2  
Old 06-11-2011, 12:04 PM
daaaave daaaave is online now
David Revelle
 
Join Date: Feb 2006
Posts: 2,963
Default

I'm not including Jack and Jill in the risk set when trying to make an estimate about them. I'll reword the problem to make it clearer.
__________________

Follow us on Twitter, Facebook, and LinkedIn
Reply With Quote
  #3  
Old 06-11-2018, 12:31 PM
ericp ericp is offline
Member
 
Join Date: Aug 2007
Posts: 262
Default

This is the most recent post on this problem that I could find. I still don't understand how the survival for Jack is 1/3 (assuming then I could figure out Jill).
If I back out to find H from S= 1/3 I get H = -1.098612289.
that is close to 1/7 + 1/6 + 1/5 + 1/4 + 1/3 which makes sense to me only if both Jack and Jill ran beyond 70 laps.
I really have no clue how this problem was solved. The solution just says "the probability that jack runs 50 or more laps is e^-1/3." But How?
Reply With Quote
  #4  
Old 06-11-2018, 01:57 PM
daaaave daaaave is online now
David Revelle
 
Join Date: Feb 2006
Posts: 2,963
Default

We are given that Jack ran at least 35 laps. If we start a Nelson-Aalen estimate, looking only at what happens after time 35, there are 3 data points (45, 55, and 70), only one of which is below 50, giving a value of H-hat of 1/3, for S-hat = e^{-1/3}.

If you don't feel comfortable starting at 35, you could say that the estimated P[X>50 | X>35] is S-hat(50)/ S-hat(35), and H-hat(50) = 1/5 + 1/4 + 1/3, while H-hat(35) = 1/5 + 1/4, so S-hat(50)/S-hat(35) = e^{-(1/5+1/4+1/3)}/e^{-(1/5+1/4)} = e^{-1/3}. See near the end of C.2.4 for a comparison of these two approaches for conditional problems.

There's also a lengthy discussion of this at http://www.theinfiniteactuary.com/mb...=19590&t=18866
__________________

Follow us on Twitter, Facebook, and LinkedIn
Reply With Quote
Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off


All times are GMT -4. The time now is 07:42 PM.


Powered by vBulletin®
Copyright ©2000 - 2018, Jelsoft Enterprises Ltd.
*PLEASE NOTE: Posts are not checked for accuracy, and do not
represent the views of the Actuarial Outpost or its sponsors.
Page generated in 0.22734 seconds with 9 queries