Actuarial Modelling of Claim Counts Risk Classification, Credibility ...

210 Actuarial Modelling of Claim Counts
Table 4.24 Transition rules for the scale −1/ + 2 scale of
Taylor (1997) with 9 levels.
Starting level
Level occupied if
0 1 2 3 ≥ 4
claim is/are reported
8 7 8 8 8 8
7 6 8 8 8 8
6 5 8 8 8 8
5 4 7 8 8 8
4 3 6 8 8 8
3 2 5 7 8 8
2 1 4 6 8 8
1 0 3 5 7 8
0 0 2 4 6 8
Table 4.25
Distances between L 1 = l 1 and L 2 = l 2 for the three metrics.
d K
l 2 l 1 0 1 2 3 4 5 6 7 8
0 0042 0377 0404 0574 0613 0701 0740 0790 0825
1 0323 0016 0044 0245 0299 0421 0483 0562 0625
2 0357 0061 0036 0200 0254 0376 0439 0520 0585
3 0396 0110 0080 0153 0204 0325 0388 0471 0539
4 0439 0168 0137 0105 0151 0267 0330 0414 0483
5 0488 0237 0207 0061 0097 0202 0262 0344 0414
d TV
l 2 l 1 0 1 2 3 4 5 6 7 8
0 0089 0754 0808 1148 1225 1402 1481 1580 1651
1 0646 0081 0107 0490 0599 0841 0966 1125 1249
2 0715 0123 0094 0402 0508 0751 0878 1041 1172
3 0791 0220 0160 0320 0411 0649 0777 0943 1078
4 0877 0337 0274 0270 0324 0535 0660 0827 0966
5 0976 0475 0413 0281 0286 0426 0527 0688 0834
d E
l 2 l 1 0 1 2 3 4 5 6 7 8
0 0001 0308 0391 1077 1415 2329 3093 4349 5908
1 0314 0002 0001 0194 0351 0863 1350 2215 3362
2 0440 0021 0006 0114 0239 0682 1120 1917 2993
3 0624 0074 0041 0044 0132 0489 0868 1584 2572
4 0902 0186 0131 0003 0041 0291 0596 1207 2085
5 1377 0430 0343 0030 0000 0100 0301 0765 1489