Actuarial Outpost Neg Binomial/exactly 2 over 3250 problem
 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

#1
05-18-2006, 07:57 PM
 stained Join Date: Apr 2006 Posts: 9
Neg Binomial/exactly 2 over 3250 problem

Is this a really tough one, or am I just missing the point?
I vaguely recall the problem says number of claims follow Negative Binomial distribution(parameters forgotten). Losses are uniformly distributed between 0 and 500. Then each payment is subject to a \$2000 deductible and a 80% coinsurance ratio. They asked for the probability of exactly 2 payments over 1000 (corresponding to exactly 2 losses over \$3250).

I listed the first 10 terms and added them up, by which I knew it should either be E or D. I chose D in the end. Anyone knew exactly how to solve the problem analytically?
#2
05-18-2006, 08:01 PM
 Bamafan Member SOA AAA Join Date: Oct 2005 Location: Sabanation Studying for Life after exams Posts: 2,525

Quote:
 Originally Posted by stained Is this a really tough one, or am I just missing the point? I vaguely recall the problem says number of claims follow Negative Binomial distribution(parameters forgotten). Losses are uniformly distributed between 0 and 500. Then each payment is subject to a \$2000 deductible and a 80% coinsurance ratio. They asked for the probability of exactly 2 payments over 1000 (corresponding to exactly 2 losses over \$3250). I listed the first 10 terms and added them up, by which I knew it should either be E or D. I chose D in the end. Anyone knew exactly how to solve the problem analytically?
I think you could modify the negative binomial by saying that beta* = prob(3250<X<5000)*beta. I don't remember the params either. This makes the answer = p_2 with beta* and r.
__________________
Sorry, I can't hear you over the sound of how awesome I am.

There is no charge for awesomeness... or attractiveness.
#3
05-18-2006, 08:07 PM
 eric57791 Member SOA Join Date: Dec 2004 Location: Texas Studying for FSA Favorite beer: Stella, Shiner, Ranger Creek Posts: 104

I believe it was r=2 and beta=3
#4
05-18-2006, 08:08 PM
 remilard Member Join Date: May 2005 Favorite beer: Talschänke Wöllnitzer Weißbier Posts: 9,539

I think you ended up with beta'=1.05 and r = 2. Not sure what the numerical answer was.
#5
05-18-2006, 08:13 PM
 shadyridr Member Join Date: Oct 2005 Location: Staten Island Posts: 6,745

I got Beta 1.75
#6
05-18-2006, 08:18 PM
 shadyridr Member Join Date: Oct 2005 Location: Staten Island Posts: 6,745

It was a UD bet. (0, 5000). The deductible was 2000 making the UD (0, 3000). A coinsurance of 80% making the UD (0, 2400). They asked find the probability that there are exactly 2 claims over the size of 1000. 1-1000/2400 = .5833333 * Beta = (now I get 1.1666666666). Maybe Im confusing this with another problem. Anyway I remember getting an answer listed so I was happy.
#7
05-18-2006, 09:09 PM
 IAGREE Join Date: Aug 2005 Posts: 17

Quote:
 Originally Posted by shadyridr It was a UD bet. (0, 5000). The deductible was 2000 making the UD (0, 3000). A coinsurance of 80% making the UD (0, 2400). They asked find the probability that there are exactly 2 claims over the size of 1000. 1-1000/2400 = .5833333 * Beta = (now I get 1.1666666666). Maybe Im confusing this with another problem. Anyway I remember getting an answer listed so I was happy.

I think this is correct, dedectible will lower the upper limit of UD instead of raiseing the lower one..
#8
05-18-2006, 09:18 PM
 Abraham Weishaus Member SOA AAA Join Date: Oct 2001 Posts: 6,195

Quote:
 Originally Posted by shadyridr It was a UD bet. (0, 5000). The deductible was 2000 making the UD (0, 3000). A coinsurance of 80% making the UD (0, 2400). They asked find the probability that there are exactly 2 claims over the size of 1000. 1-1000/2400 = .5833333 * Beta = (now I get 1.1666666666). Maybe Im confusing this with another problem. Anyway I remember getting an answer listed so I was happy.
Wrong.

The probability of a loss over 3250 is 1750/5000=0.35, and that is what beta gets multiplied by.

Your logic simply doesn't work. After the deductible, it is no longer uniform; it has a point mass at 0.
#9
05-18-2006, 09:23 PM
 AmInEm Member SOA Join Date: May 2005 Location: Montreal, QC Studying for FETE Posts: 431

exactly I got a Beta* = 3*0.35 = 1.05. and I believe it gave the right answer.
#10
05-18-2006, 09:38 PM
 IAGREE Join Date: Aug 2005 Posts: 17

Quote:
 Originally Posted by Abraham Weishaus Wrong. The probability of a loss over 3250 is 1750/5000=0.35, and that is what beta gets multiplied by. Your logic simply doesn't work. After the deductible, it is no longer uniform; it has a point mass at 0.

I remembre there was one question on previous exam (couldnt remember which year though), something like UD (0, 10) changes to (0, 6), after 4 deductible...

 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 10:15 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