Estimation, Evaluation, and Selection of Actuarial Models
Estimation, Evaluation, and Selection of Actuarial Models
Estimation, Evaluation, and Selection of Actuarial Models
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76 CHAPTER 4. MODEL EVALUATION AND SELECTION<br />
j y j F ∗ (x) F n (x) summ<strong>and</strong><br />
0 50 0.0000 0.0000 0.0399<br />
1 82 0.0391 0.0526 0.0388<br />
2 115 0.0778 0.1053 0.0126<br />
3 126 0.0904 0.1579 0.0332<br />
4 155 0.1227 0.2105 0.0070<br />
5 161 0.1292 0.2632 0.0904<br />
6 243 0.2138 0.3158 0.0501<br />
7 294 0.2622 0.3684 0.0426<br />
8 340 0.3033 0.4211 0.0389<br />
9 384 0.3405 0.4737 0.0601<br />
10 457 0.3979 0.5263 0.1490<br />
11 680 0.5440 0.5789 0.0897<br />
12 855 0.6333 0.6316 0.0099<br />
13 877 0.6433 0.6842 0.0407<br />
14 974 0.6839 0.7368 0.0758<br />
15 1,193 0.7594 0.7895 0.0403<br />
16 1,340 0.7997 0.8421 0.0994<br />
17 1,884 0.8983 0.8947 0.0592<br />
18 2,558 0.9561 0.9474 0.0308<br />
19 3,476 0.9860 1.0000 0.0141<br />
20 ∞ 1.0000 1.0000<br />
The total is 1.0226 <strong>and</strong> the test statistic is −19(1) + 19(1.0226) = 0.4292. Because the test statistic<br />
is less than the critical value <strong>of</strong> 2.492, the exponential model is viewed as plausible.<br />
For Data Set B censored at 1,000, the results are in the following table.<br />
j y j F ∗ (x) Fn(x) ∗ summ<strong>and</strong><br />
0 0 0.0000 0.00 0.0376<br />
1 27 0.0369 0.05 0.0718<br />
2 82 0.1079 0.10 0.0404<br />
3 115 0.1480 0.15 0.0130<br />
4 126 0.1610 0.20 0.0334<br />
5 155 0.1942 0.25 0.0068<br />
6 161 0.2009 0.30 0.0881<br />
7 243 0.2871 0.35 0.0493<br />
8 294 0.3360 0.40 0.0416<br />
9 340 0.3772 0.45 0.0375<br />
10 384 0.4142 0.50 0.0575<br />
11 457 0.4709 0.55 0.1423<br />
12 680 0.6121 0.60 0.0852<br />
13 855 0.6960 0.65 0.0093<br />
14 877 0.7052 0.70 0.0374<br />
15 974 0.7425 0.75 0.0092<br />
16 1000 0.7516 0.75
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