Actuarial Outpost soa #59
 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

 Upload your resume securely at https://www.dwsimpson.com to be contacted when new jobs meet your skills and objectives.

#1
03-10-2018, 04:02 PM
 ericp Member Join Date: Aug 2007 Posts: 251
soa #59

Does anyone know of a different way of explaining why the answer choice of E is correct, specifically as it relates to the right tail being thinner?

One more question - when the solution says "the model" is it referring to the p-p plot itself or is it referring to the supposed distribution we think the data follows? I thought the former because the model, our supposed distribution, does not automatically assign more data to the values less than the left tail in all cases - sometimes more, sometimes less and sometimes nearly the same as the empirical. But then why would they call the p-p plot a "model"? It should say "the p-p plot assigns more probability..." or something similar, yes?

Thanks.
#2
03-11-2018, 01:56 AM
 dkamka Member SOA Join Date: Jul 2010 Location: Austin, Texas Studying for Predictive Analytics& FAP College: Roosevelt University Alumnus '10 Favorite beer: Jawa Juice Posts: 439

Do they mean that assigning not enough weight/probability is a thinner tail?
__________________
PM me if you’re in the Austin area
Introductory I: Economics | Accounting & FinanceFM | P
Introductory II: IFM | Mathematical Statistics
Actuarial: LTAM | STAM | SRM
Seminar: APC
#3
03-11-2018, 05:15 PM
 ericp Member Join Date: Aug 2007 Posts: 251

Yes, the p-p plot is above the 45 degree line on the chart at highest F values as it is at the lowest F values. The answer says it is too thick at lower end but then says it is too thin at higher end even though it is again above the line.
#4
03-11-2018, 09:12 PM
 daaaave David Revelle Join Date: Feb 2006 Posts: 2,943

There are two ways to think about it. What the SOA is saying is that at both the left and right tails, we have modeled (or fitted) CDF > observed CDF. The CDF itself describes the left tail, so having modeled CDF > observed CDF means the model puts too much weight on the left tail / the left tail is too thick. The right tail is about the probability of being large, so is about the survival function. If modeled CDF > observed CDF, then modeled survival function < observed survival function, so the model is putting too little weight on the right tail / the right tail is too thin.

Another way to think about it is not to think about whether we are above or below the line y=x, but rather what is the slope in a given region. When the slope is above 1, the model CDF is increasing faster than the observed, so we are predicting more data than observed and putting too much weight. When the slope is below 1, the model CDF is increasing more slowly than the observed, and we are predicting too little there and thus are putting in too little weight. In the left tail, our slope is much larger than 1 initially, hence we have too much weight on the left tail. In the right tail, the slope is less than 1, so we have too little weight there and the modeled / fitted right tail is too thin.
__________________

#5
03-14-2018, 10:09 AM
 ericp Member Join Date: Aug 2007 Posts: 251

Thank You. Thinking about the slope really helps to make it more clear.

 Thread Tools Display Modes Linear 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 12:12 AM.

 -- 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