00:01
Okay, so we'll use the buhmann credibility approach here.
00:08
And here we have the class 1, poison with lambda equals 5, mean lambda equals 5 for class 2 binomial distribution, with m equals 8, q equals 0 .55.
00:27
And it means that the mean is mq or 4 .4.
00:43
And so the overall mean is mu equals 5 plus 4 .4 over 2 which is equal to 4 .7 and for class 1 the variance is also equal to lambda so that's 5.
01:10
For class 2 the variance is mq times 1 minus q which is equal to 1 .98 and so since the risks are equally divided between the two classes we have sigma the overall variance is sigma 1 squared plus sigma 2 squared over 2 5 plus 1 .98 over 2 3 .49 and the credibility factor z is given by n s squared over n s squared plus sigma squared where n is the number of years of the data and s squared is a sample variance of the claims for the risk under consideration.
02:14
So here we have n equals 3, year 1, 2, and 3.
02:18
Now we calculate s squared first.
02:27
That is 3 minus x bar squared plus r minus x bar squared plus 4 minus x bar squared over 3 3 -1, where x bar is equal to 3 plus r plus 4 over 3, 7 plus r...