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#1
05-19-2012, 12:34 PM
 oofta Member SOA Join Date: Sep 2010 Posts: 2,131
TIA PE4 #25

You observe two loss for amounts 5 and 7 for one insured. Find the Bulmann credibility estimate for the third loss for that insured.

This is not the entire question. I was able to find a,v, mu, and xbar just fine. I am curious why we set n=2 in P_c? I was thinking that there was only one exposure since there is only one insured.
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Quote:
 Originally Posted by Smart Actuary Alpha donkey FTW
#2
05-19-2012, 03:46 PM
 truonda Member SOA Join Date: Apr 2012 Studying for MLC College: Waterloo Alumni Posts: 186

I just remember that the n in Buhlmann's k is always the same as the n used to calculate xbar. Hope that helps.
#3
05-19-2012, 03:52 PM
 killjacker Member Join Date: Sep 2010 Location: Illinois Posts: 34

One exposure is not equal to one insured, it's equal to one insured-year. You have 2 insured-years, so there are 2 exposure units.
#4
05-21-2012, 11:48 AM
 home_alone Member Join Date: Nov 2008 Posts: 242

Quote:
 Originally Posted by truonda I just remember that the n in Buhlmann's k is always the same as the n used to calculate xbar. Hope that helps.
Be careful. This is not always the case. There are some situations where it is not true.
#5
05-21-2012, 11:58 AM
 truonda Member SOA Join Date: Apr 2012 Studying for MLC College: Waterloo Alumni Posts: 186

Quote:
 Originally Posted by home_alone Be careful. This is not always the case. There are some situations where it is not true.
Can you provide an example? (so I don't fall into my own trap)

EDIT: I know that if you need to calculate an estimate for a specific group then n becomes the n used to calculate xbar for that group. Could this be what you were talking about?

Last edited by truonda; 05-21-2012 at 12:02 PM..
#6
05-21-2012, 12:15 PM
 home_alone Member Join Date: Nov 2008 Posts: 242

Quote:
 Originally Posted by truonda Can you provide an example? (so I don't fall into my own trap) EDIT: I know that if you need to calculate an estimate for a specific group then n becomes the n used to calculate xbar for that group. Could this be what you were talking about?

Quote:
 Originally Posted by MoProblems_MoMoney I always make a last minute formula sheet / reminder list to look over before an actuarial exam. I thought I'd share what's on mine and see if anyone else has something similar. Match Buhlmann n to the # of "units" where Pc is calculated per "unit" Look for conditional variance formula (any time a parameter is unknown with a known distribution) Read NA-KM problems for NA/KM and F/S/H, carefully Bootstrap E[(A-B)^2] where A is a stupid estimator and varies in each case, B is constant and a smart estimator "Like X^2 but Smirnoffed Darling is needy" -- Likelihood and chi square are robust and do not need adjustment but Smirnoff and Anderson Darling need a lot adjusting of critical values "Darling is a slut" - no adjustment as n->infinity and heavy on tail weight estimation. Watch S(x) for >= vs > bounds In any deductible problem, look for CONDITIONING! Be slow and thorough!
I don't have an example but here is what I got from previous discussion on this issue. See the first bullet point.
#7
05-21-2012, 12:49 PM
 truonda Member SOA Join Date: Apr 2012 Studying for MLC College: Waterloo Alumni Posts: 186

I still don't think there is anything wrong with my logic.
#8
05-21-2012, 02:23 PM
 home_alone Member Join Date: Nov 2008 Posts: 242

If it does work for you then you keep it then. It is yours. But remember it does not work in semiparametric cases for example and some other cases too.

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