I have the following past exam question:
A group of 340 insureds in a high-crime area submit the 210 theft claims in a one-year period as given in the table below. Each insured is assumed to have a Poisson distribution for the number of thefts, but the mean of such a distribution may vary from one insured to another. If a particular insured experienced two claims in the observation period, determine the Buhlmann credibility estimate for the number of claims for this insured in the next period.
Table:
No of claims No. of insureds
0 200
1 80
2 50
3 10
In the solution to this problem a^ = 817/1156-21/34=817/1156=0.706747
But shouldn't a^= 0.7088322 (that is, shouldn't we divide the sample variance by r-1=339)? Why does he divide it by r=340?
Many thanks
A group of 340 insureds in a high-crime area submit the 210 theft claims in a one-year period as given in the table below. Each insured is assumed to have a Poisson distribution for the number of thefts, but the mean of such a distribution may vary from one insured to another. If a particular insured experienced two claims in the observation period, determine the Buhlmann credibility estimate for the number of claims for this insured in the next period.
Table:
No of claims No. of insureds
0 200
1 80
2 50
3 10
In the solution to this problem a^ = 817/1156-21/34=817/1156=0.706747
But shouldn't a^= 0.7088322 (that is, shouldn't we divide the sample variance by r-1=339)? Why does he divide it by r=340?
Many thanks
Buhlman credibility
