Two insureds own delivery vans. Insured A had two vans in year 1 and one claim, two vans in year 2 and one claim, and one van in year 3 with no claims. Insured B has no vans in year 1, three vans in year 2 and two claims, and two vans in year 3 and three claims. The number of claims for insured each year has a Poisson distribution. Use semiparametric empirical Bayes estimation to obtain the estimated number of claims for each insured in year 4.

For A: 2.208

For B: 2.9024

Step-by-step explanation:

To solve we will do the following:

For A:

no insured (x) claims (y) xy Var=total / (y-1)

2 1 2 0.08

2 1 2 0.08

1 0 0 0.64

Weighted average 0.8 0.16

a var - X - 0.64

k mean/a - 1.25

Z (credibility) 1 / (1+k) 0.444

no of claims for next year (y=4)

= 0.44*4 + 0.56*0.8

= 2.208

For B:

no insured (x) claims (y) xy Var=total / (y-1)

0 0 0 0

3 6 12 12

2 3 6 2

Weighted average 2.4 3.5

a var - X 1.1

k mean/a 2.18

Z (credibility) 1 / (1+k) 0.314

no of claims for next year (y=4)

0.314*4 + 0.686*2.4

= 2.9024