Actuarial Outpost
 
Go Back   Actuarial Outpost > Exams - Please Limit Discussion to Exam-Related Topics > SoA/CAS Preliminary Exams > Short-Term Actuarial Math
FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

2017 ACTUARIAL SALARY SURVEYS
Contact DW Simpson for a Personalized Salary Survey

Short-Term Actuarial Math Old Exam C Forum

Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 01-23-2015, 02:13 PM
trondogss's Avatar
trondogss trondogss is offline
Member
SOA
 
Join Date: Nov 2005
Location: Master Control Program
Studying for GH Specialty
Posts: 8,304
Default Maximum Likelihood Question: Ground Up

I always get confused on what Ground Up means when doing a Maximum Likelihood (MLE) question. Particularly, I worked a problem that read as such (some stuff changed for potential copyright issues:

There is a deductible of 1 and maximum covered loss of 20:
Observe the following Payments: 3, 6, 17, 19
Fit ground-up exponential distribution using MLE.
What is the mean of the fitted distribution?

____________________________

So, when I solved this problem, I took the payments, and converted it to losses (4, 7, 18, 20+). Then used the losses to find my fitted parameter.

So...why does the solution to this problem use the payments to solve for the parameter and not the losses? Thanks in advance for the help.
__________________
P FM MFE MLC Modules 1-8 IA FA C ASA GH Core GH Advanced FSA Modules 1/3
Quote:
Originally Posted by Vomik View Post
You successfully played "just the tip?" Ive always ended up losing
Reply With Quote
  #2  
Old 01-23-2015, 02:26 PM
Gandalf's Avatar
Gandalf Gandalf is offline
Site Supporter
Site Supporter
SOA
 
Join Date: Nov 2001
Location: Middle Earth
Posts: 30,945
Default

You should get the same result if you work with losses, as long as your formulas reflect that you have no information about losses less than one. For some other distributions (not here - exponential is memoryless) you would have to work with losses.
Reply With Quote
  #3  
Old 01-23-2015, 02:31 PM
Abelian Grape's Avatar
Abelian Grape Abelian Grape is offline
Meme-ber                         Meme-ber
CAS
 
Join Date: Jul 2014
Favorite beer: Allagash Curieux
Posts: 41,585
Default

Quote:
Originally Posted by actuary_aspire
Memoryless?
http://en.wikipedia.org/wiki/Memorylessness
__________________
Quote:
Originally Posted by Pension.Mathematics View Post
what's your problem man?
Reply With Quote
  #4  
Old 01-23-2015, 02:34 PM
actuary_aspire actuary_aspire is offline
Member
CAS
 
Join Date: Sep 2009
Posts: 3,979
Default

Quote:
Originally Posted by Abelian Grape View Post
I know. I was answering the OP's question with a question, but then saw that Gandalf had a better response, so I deleted the post.

tl;dr ninja'd
Reply With Quote
  #5  
Old 01-23-2015, 02:36 PM
Abelian Grape's Avatar
Abelian Grape Abelian Grape is offline
Meme-ber                         Meme-ber
CAS
 
Join Date: Jul 2014
Favorite beer: Allagash Curieux
Posts: 41,585
Default

i ninja'd you before you can undo gandalf ninja-ing you
__________________
Quote:
Originally Posted by Pension.Mathematics View Post
what's your problem man?
Reply With Quote
  #6  
Old 01-23-2015, 03:06 PM
actuary_aspire actuary_aspire is offline
Member
CAS
 
Join Date: Sep 2009
Posts: 3,979
Default

Quote:
Originally Posted by Abelian Grape View Post
i ninja'd you before you can undo gandalf ninja-ing you
right place at the right time.

also known as ninja.
Reply With Quote
  #7  
Old 01-23-2015, 03:49 PM
trondogss's Avatar
trondogss trondogss is offline
Member
SOA
 
Join Date: Nov 2005
Location: Master Control Program
Studying for GH Specialty
Posts: 8,304
Default

Quote:
Originally Posted by Gandalf View Post
You should get the same result if you work with losses, as long as your formulas reflect that you have no information about losses less than one. For some other distributions (not here - exponential is memoryless) you would have to work with losses.
great thanks, I forgot to divide by S(1).
__________________
P FM MFE MLC Modules 1-8 IA FA C ASA GH Core GH Advanced FSA Modules 1/3
Quote:
Originally Posted by Vomik View Post
You successfully played "just the tip?" Ive always ended up losing
Reply With Quote
  #8  
Old 01-23-2015, 06:16 PM
Jim Daniel's Avatar
Jim Daniel Jim Daniel is offline
Member
SOA
 
Join Date: Jan 2002
Location: Davis, CA
College: Wabash College B.A. 1962, Stanford Ph.D. 1965
Posts: 2,675
Default

You really need to know that the amount paid per positive payment when there is only a deductible and the ground-up loss is Exponential is itself an Exponential with the same mean as the ground-up loss. Thus, just considering the amount per payment with the deductible, you observed values of 3, 6, 17, and 19+. But for an Exponential this makes the MLE equal (3 + 6 + 17 + 19) / 3 = 15. You're done.

Jim Daniel
__________________
Jim Daniel
Jim Daniel's Actuarial Seminars
www.actuarialseminars.com
jimdaniel@actuarialseminars.com
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 09:13 AM.


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 0.20341 seconds with 11 queries