| Main Calculations for Class Rates |
|
(1) |
(2) |
(3) |
(4) |
(5) |
(6) |
(7) |
(8) |
(9) |
(10) |
(11) |
(12) |
| \(i\) |
\(e_i\) |
\(l_i\) |
\(L_i\) |
\(c_i\) |
\(Z_i\) |
\(Z_iL_i +(1-Z_i)M\) |
\(Z_iL_i +(1-Z_i)M \times e_i\) |
\(e_i(1-Z_i)\) |
\(e_i(1-Z_i)M\times C\) |
\(e_i\times r_i\) |
\(final \ r_i\) |
\(old \ r_i\) |
|
(Data) |
(Data) |
(1)/(2) |
(1)\(\times\)C |
Sqrt((4)/683) |
(3)\(\times\)(5)+A(1.0-(5)) |
(6)\(\times\)(1) |
((1)\(\times\)(1.0-(5))\(\times\)A |
(8)\(\times\)H |
(5)\(\times\)(3)\(\times\)(1)+(9) |
(5)\(\times\)(10)/(1) |
Table 2 Col. 7 |
| Class |
Exposure |
Losses |
Raw Rate "L" |
Expected Claim Count |
Credibility of Class |
Credibility Adjusted Rate |
Losses in Adjusted Rates |
Losses From Complement of Credibility |
Complement Losses After Off-Balance Correction |
Off-Balance Corrected Total Losses |
Off-Balance Corrected (Rate |
Indications Under Old (Off-Balance |
| 1 |
25 |
$ 78,427 |
$ 3,137 |
65 |
31 % |
$ 1,324 |
$ 33,097 |
$ 8,958 |
$ 15,465 |
$ 39,605 |
$ 1,584 |
$ 1564 |
| 2 |
30 |
$ 40,687 |
$ 1,356 |
78 |
34 % |
$ 800 |
$ 24,012 |
$ 10,293 |
$ 17,771 |
$ 31,489 |
$ 1,050 |
$ 946 |
| 3 |
36 |
$ 65,073 |
$ 1,808 |
93 |
37 % |
$ 994 |
$ 35,787 |
$ 11,752 |
$ 20,290 |
$ 44,324 |
$ 1,231 |
$ 1,174 |
| 4 |
43 |
$ 35,837 |
$ 830 |
112 |
40 % |
$ 644 |
$ 27,814 |
$ 13,314 |
$ 22,986 |
$ 37,486 |
$ 868 |
$ 761 |
| 5 |
52 |
$ 59,918 |
$ 1,156 |
134 |
44 % |
$ 800 |
$ 41,498 |
$ 14,941 |
$ 25,795 |
$ 52,352 |
$ 1,010 |
$ 946 |
| 6 |
62 |
$ 72,435 |
$ 1,164 |
161 |
49 % |
$ 832 |
$ 51,736 |
$ 16,567 |
$ 28,602 |
$ 63,771 |
$ 1,025 |
$ 983 |
| 7 |
75 |
$ 63,990 |
$ 857 |
193 |
53 % |
$ 698 |
$ 52,124 |
$ 18,089 |
$ 31,231 |
$ 65,265 |
$ 874 |
$ 825 |
| 8 |
90 |
$ 57,059 |
$ 637 |
232 |
58 % |
$ 587 |
$ 52,598 |
$ 19,353 |
$ 33,413 |
$ 66,657 |
$ 744 |
$ 694 |
| 9 |
107 |
$ 90,110 |
$ 838 |
278 |
64 % |
$ 722 |
$ 77,642 |
$ 20,130 |
$ 34,753 |
$ 92,265 |
$ 858 |
$ 853 |
| 10 |
129 |
$ 46,934 |
$ 364 |
334 |
70 % |
$ 410 |
$ 52,902 |
$ 20,088 |
$ 34,681 |
$ 67,495 |
$ 523 |
$ 485 |
| 11 |
155 |
$ 47,281 |
$ 305 |
401 |
77 % |
$ 355 |
$ 54,971 |
$ 18,759 |
$ 32,386 |
$ 68,598 |
$ 443 |
$ 420 |
| 12 |
186 |
$ 54,427 |
$ 293 |
481 |
84 % |
$ 329 |
$ 61,145 |
$ 15,482 |
$ 26,728 |
$ 72,392 |
$ 390 |
$ 389 |
| 13 |
223 |
$ 69,726 |
$ 313 |
577 |
92 % |
$ 329 |
$ 73,422 |
$ 9,338 |
$ 16,122 |
$ 80,206 |
$ 360 |
$ 389 |
| 14 |
267 |
$ 64,108 |
$ 240 |
692 |
100 % |
$ 240 |
$ 64,108 |
- |
- |
$ 64,108 |
$ 240 |
$ 283 |
| 15 |
321 |
$ 86,197 |
$ 269 |
831 |
100 % |
$ 269 |
$ 86,197 |
- |
- |
$ 86,197 |
$ 269 |
$ 317 |
| |
|
|
|
|
|
|
|
|
|
|
|
|
| Total |
1,801 |
$ 932,211 |
$ 518 |
4,661 |
|
$ 438 |
$ 789,053 |
$ 197,065 |
$ 340,223 |
$ 932,211 |
$ 518 |
$ 518 |
| Reference Values for All Classes |
|
A =Needed Overall Average Rate |
$ 518 |
|
|
B = Severity (Computed Outside the Table) |
$ 200 |
|
|
C = A/B = Expected Claims/Exposure |
2.588 |
|
|
D = Total Losses in Data |
$ 932,211 |
|
|
E = Total Losses in Adjusted Rates |
$ 789,053 |
|
|
F = D-E = Off-Balance in $ |
$ 143,158 |
|
|
G = Total Losses in \((1-Z_i)\) Term |
$ 197,065 |
|
|
H = 1.0+F/G = Off-Balance Factor |
1.742 |
|