Actuarial Outpost ASM 22.2 Likelihood Ratio Algorithm
 Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read
 FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

 D.W. Simpson & Company International Actuary Jobs   Canada  Asia  Australia  Life  Pension  CasualtyBermuda, United Kingdom, Europe, Asia, Worldwide

#1
04-10-2007, 08:18 AM
 GoBolts Member Join Date: Oct 2004 Posts: 295
ASM 22.2 Likelihood Ratio Algorithm

(22.2 From the 4th edition)

The question lists loglikelihoods for 1,2,3,4,5 parameter distributions. Using 95% confidence how many parameters are in the selected model.

In the solution it compares 2(1param-2param) to the value in the chi sq table, then it compares 2(1param-3param) and then 2(1param-4param). The 4 param distribution is the first which twice the difference in the loglikelihoods is greater than the value from the table. Then when you test the 5 parameter distribution the solution is comparing 2(4param-5param).

What is the process when you are moving up through adding new parameters. Is it as follows: You start off assuming the simplist 1 parameter distribution. Then you add parameters if they are deemed worth it by the test. Then once you find one that is worth it, that becomes your new starting point for comparing and adding more parameters?
#2
04-10-2007, 09:15 AM
 Kabaka Member SOA Join Date: Aug 2006 Location: O Canada Studying for NOTHING! :) Favorite beer: Root Posts: 2,185

Quote:
 Originally Posted by GoBolts What is the process when you are moving up through adding new parameters. Is it as follows: You start off assuming the simplist 1 parameter distribution. Then you add parameters if they are deemed worth it by the test. Then once you find one that is worth it, that becomes your new starting point for comparing and adding more parameters?
That's how I understand it.
#3
04-10-2007, 11:12 AM
 Kazodev Member SOA Join Date: May 2004 Posts: 3,393

The theory is basically you have a tradeoff between fit and complexity. So if you wanted you could pick a distribution with 200 parameters and it would fit your data perfectly but is that really what you shoul do? What if you picked a distribution with 3 paramters and it fit 98% of your data? So there are different ways to penalize for adding paramters, loglikelihood is one, AIC(BIC) is another one, etc.

 Thread Tools Display Modes Hybrid Mode

 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 01:31 PM.

 -- Default Style - Fluid Width ---- Default Style - Fixed Width ---- Old Default Style ---- Easy on the eyes ---- Smooth Darkness ---- Chestnut ---- Apple-ish Style ---- If Apples were blue ---- If Apples were green ---- If Apples were purple ---- Halloween 2007 ---- B&W ---- Halloween ---- AO Christmas Theme ---- Turkey Day Theme ---- AO 2007 beta ---- 4th Of July Contact Us - Actuarial Outpost - Archive - Privacy Statement - Top