Neg Binomial/exactly 2 over 3250 problem

[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?

[Bamafan]

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.

[eric57791]

I believe it was r=2 and beta=3

[remilard]

I think you ended up with beta'=1.05 and r = 2. Not sure what the numerical answer was.

[shadyridr]

I got Beta 1.75

[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.

[IAGREE]

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..

[Abraham Weishaus]

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.

[AmInEm]

exactly I got a Beta* = 3*0.35 = 1.05. and I believe it gave the right answer.

[IAGREE]

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...