Actuarial Outpost soa #59
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#1
03-10-2018, 04:02 PM
 ericp Member Join Date: Aug 2007 Posts: 262
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 CAS SOA Join Date: Jul 2010 Location: Austin, Texas Studying for Predictive Analytics& FAP College: Roosevelt University Alumnus '10 Favorite beer: Jawa Juice Posts: 450

Do they mean that assigning not enough weight/probability is a thinner tail?
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#3
03-11-2018, 05:15 PM
 ericp Member Join Date: Aug 2007 Posts: 262

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: 2,963

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.
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#5
03-14-2018, 10:09 AM
 ericp Member Join Date: Aug 2007 Posts: 262

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