| First Step: Calculation of Basic Variance Parameters |
|
I. Sum of Squared Differences from Sample Means Within Classes "\(i\)" = \(\alpha^2\) = |
7.379E+9 |
|
|
II. Sum of Exposures Times Squared Differences Between Class Sample Means "\(L_i\)'s" and Overall Mean "\(M\)" = \(\beta^2\) = |
3.941E+8 |
|
|
III. = I./((total(1)-15(="\(n\)"))=Process Variance = \(s^2\) = |
4,131,869 |
|
|
IV. = [II.- (\(n\)-1.0)III.]/[total(1)-\(\sum_{i=1}^{15}e_i^2\)/total(1)]= Variance of Hypothetical Means = \(\sigma^2\) = |
208,304 |
|
|
V. III./IV = Credibility Constant=\(K\) = |
19.84 |
|
| Second Step: Main Calculations for Class Rates |
|
(1) |
(2) |
(3) |
(4) |
(5) |
(6) |
(7) |
(8) |
(9) |
(10) |
| \(i\) |
\(e_i\) |
\(l_i\) |
\(L_i\) |
\(Z_i\) |
\(Z_iL_i+(1-Z_i)M\) |
\([Z_iL_i+(1-Z_i)M]\times e_i\) |
\(e_i(1-Z_i)\) |
\(e_i(1-Z_i)M\times C\) |
\( e_i\times r_i]\) |
\(final \ r_i\) |
|
(Data) |
(Data) |
(1)/(2) |
(1)/((1)+V.) |
(3)\(\times\)(4)+A\(\times\)(1.0-(4)) |
(5)\(\times\)(1) |
(1) \(\times\) (1.0-(4)) |
(7)\(\times\)A\(\times\)F |
(6)+(8) |
(5)\(\times\)(9)/(1) |
| Class |
Exposure |
Losses |
Raw Rate "l" |
Credibility of Class |
Credibility Adjusted Rate |
Losses in Adjusted Rates |
Off-Balance Correction Basis |
Additional Losses From Off-Balance Correction |
Off-Balance Corrected Total Losses |
Off-Balance Corrected (Rate |
| 1 |
25 |
$ 78,427 |
$ 3,137 |
56 % |
$ 1,978 |
$ 49,456 |
$ 11 |
$ 3,162 |
$ 52,617 |
$ 2,105 |
| 2 |
30 |
$ 40,687 |
$ 1,356 |
60 % |
$ 1,022 |
$ 30,674 |
$ 12 |
$ 3,413 |
$ 34,087 |
$ 1,136 |
| 3 |
36 |
$ 65,073 |
$ 1,808 |
64 % |
$ 1,349 |
$ 48,576 |
$ 13 |
$ 3,656 |
$ 52,232 |
$ 1,451 |
| 4 |
43 |
$ 35,837 |
$ 830 |
69 % |
$ 731 |
$ 31,596 |
$ 14 |
$ 3,886 |
$ 35,482 |
$ 821 |
| 5 |
52 |
$ 59,918 |
$ 1,156 |
72 % |
$ 979 |
$ 50,762 |
$ 14 |
$ 4,101 |
$ 54,863 |
$ 1,058 |
| 6 |
62 |
$ 72,435 |
$ 1,164 |
76 % |
$ 1,008 |
$ 62,708 |
$ 15 |
$ 4,299 |
$ 67,007 |
$ 1,077 |
| 7 |
75 |
$ 63,990 |
$ 857 |
79 % |
$ 786 |
$ 58,669 |
$ 16 |
$ 4,480 |
$ 63,149 |
$ 846 |
| 8 |
90 |
$ 57,059 |
$ 637 |
82 % |
$ 615 |
$ 55,121 |
$ 16 |
$ 4,642 |
$ 59,764 |
$ 667 |
| 9 |
107 |
$ 90,110 |
$ 838 |
84 % |
$ 788 |
$ 84,741 |
$ 17 |
$ 4,787 |
$ 89,528 |
$ 833 |
| 10 |
129 |
$ 46,934 |
$ 364 |
87 % |
$ 384 |
$ 49,578 |
$ 17 |
$ 4,914 |
$ 54,492 |
$ 422 |
| 11 |
155 |
$ 47,281 |
$ 305 |
89 % |
$ 330 |
$ 51,012 |
$ 18 |
$ 5,026 |
$ 56,038 |
$ 362 |
| 12 |
186 |
$ 54,427 |
$ 293 |
90 % |
$ 315 |
$ 58,453 |
$ 18 |
$ 5,123 |
$ 63,576 |
$ 342 |
| 13 |
223 |
$ 69,726 |
$ 313 |
92 % |
$ 330 |
$ 73,457 |
$ 18 |
$ 5,207 |
$ 78,664 |
$ 353 |
| 14 |
267 |
$ 64,108 |
$ 240 |
93 % |
$ 259 |
$ 69,241 |
$ 18 |
$ 5,279 |
$ 74,520 |
$ 279 |
| 15 |
321 |
$ 86,197 |
$ 269 |
94 % |
$ 283 |
$ 90,850 |
$ 19 |
$ 5,340 |
$ 96,191 |
$ 300 |
|
|
|
|
|
|
|
|
|
|
|
| Total |
1,801 |
$ 932,211 |
$ 518 |
|
$ 480 |
$ 864,895 |
$ 235 |
$ 67,315 |
$ 932,211 |
$ 518 |
| Reference Values for All Classes |
|
A = Overall Average Rate |
$ 518 |
|
|
B = Total Loss in Credibility Adjusted Rates |
$ 864,895 |
|
|
C= Total Losses in Data |
$ 932,211 |
|
|
D = C-B = Shortfall |
$ 67,315 |
|
|
E =Total Off-Balance Correction Basis |
$ 235 |
|
|
F = D/E = Off-Balance Factor |
285.86 |
|