Skip to main content
. 2010 Apr 8;10:31. doi: 10.1186/1471-2288-10-31

Table 3.

TDI simulation results

Mean MSE × 1000 EC
p n log(κp) Lin Ch. PI Lin Ch. PI Lin Ch. TI
μD = 0 0.80 20 1.981 2.014 1.977 1.985 10.409 8.492 8.496 95.7 94.7 98.5
σD = 5.65 100 1.997 1.980 1.981 2.040 1.617 1.615 97.4 94.8 98.5
0.85 20 2.097 2.131 2.093 2.102 10.425 8.491 8.498 95.7 94.7 98.3
100 2.133 2.096 2.098 2.048 1.616 1.615 97.4 94.8 98.3
0.90 20 2.231 2.264 2.227 2.235 10.381 8.496 8.491 95.7 94.7 97.9
100 2.246 2.229 2.231 2.027 1.618 1.615 97.3 94.4 97.9
0.95 20 2.406 2.439 2.402 2.410 10.399 8.495 8.491 95.7 94.7 97.6
100 2.421 2.405 2.406 2.036 1.617 1.615 97.3 94.7 97.6
μD = 2.174 0.80 20 2.052 2.076 2.047 2.054 10.286 9.216 9.135 95.2 94.9 97.4
σD = 5.65 100 2.061 2.048 2.050 2.167 1.983 1.971 95.5 93.4 95.4
0.85 20 2.167 2.192 2.161 2.169 10.347 9.109 9.030 95.2 94.9 96.9
100 2.178 2.163 2.165 2.192 1.961 1.951 95.7 93.3 95.0
0.90 20 2.300 2.326 2.293 2.300 10.364 8.998 8.902 95.3 94.8 96.6
100 2.311 2.296 2.297 2.199 1.943 1.930 95.8 93.1 94.2
0.95 20 2.473 2.501 2.465 2.472 10.487 8.834 8.735 95.6 94.9 96.2
100 2.486 2.469 2.470 2.253 1.904 1.892 96.1 93.3 93.8
μD = 5 0.80 20 2.287 2.281 2.276 2.281 8.736 9.211 9.061 91.9 94.6 91.0
σD = 5.65 100 2.278 2.286 2.287 1.954 1.890 1.886 91.9 94.7 92.6
0.85 20 2.391 2.398 2.378 2.383 8.748 8.658 8.505 93.6 95.0 91.4
100 2.395 2.390 2.390 1.890 1.751 1.747 95.3 94.5 92.8
0.90 20 2.508 2.531 2.495 2.500 9.231 8.114 7.965 94.9 94.6 91.9
100 2.528 2.507 2.508 2.272 1.616 1.613 97.7 94.5 92.8
0.95 20 2.662 2.706 2.647 2.652 10.660 7.624 7.463 97.2 94.1 92.0
100 2.703 2.660 2.661 3.569 1.485 1.481 99.1 94.4 93.2
μD = 0 0.80 20 2.579 2.618 2.581 2.589 10.282 7.911 8.011 97.1 96.7 99.1
σD = 10.28 100 2.595 2.577 2.579 2.121 1.647 1.639 97.2 94.3 98.5
0.85 20 2.695 2.734 2.697 2.705 10.301 7.911 8.014 97.1 96.7 98.7
100 2.711 2.693 2.695 2.128 1.642 1.639 97.2 94.4 98.2
0.90 20 2.828 2.868 2.830 2.839 10.327 7.912 8.018 97.1 96.7 98.3
100 2.844 2.827 2.828 2.139 1.641 1.640 97.2 94.4 97.8
0.95 20 3.003 3.043 3.006 3.014 10.349 7.911 8.020 97.1 96.7 98.0
100 3.020 3.002 3.004 2.148 1.640 1.640 97.2 94.5 97.5
μD = 2.174 0.80 20 2.601 2.627 2.593 2.601 9.833 8.595 8.502 95.3 95.2 97.9
σD = 10.28 100 2.613 2.597 2.599 2.171 1.819 1.809 96.3 93.5 96.9
0.85 20 2.717 2.743 2.709 2.717 9.846 8.567 8.473 95.3 95.3 97.8
100 2.729 2.713 2.715 2.177 1.816 1.806 96.3 93.6 96.9
0.90 20 2.850 2.877 2.842 2.849 9.864 8.529 8.435 95.4 95.2 97.3
100 2.862 2.847 2.848 2.185 1.812 1.802 96.3 93.6 96.4
0.95 20 3.025 3.052 3.016 3.024 9.879 8.848 8.379 95.5 95.3 97.1
100 3.038 3.022 3.023 2.192 1.807 1.797 96.4 93.7 95.8
μD = 5 0.80 20 2.689 2.706 2.682 2.689 9.727 9.684 9.550 93.6 94.1 95.8
σD = 10.28 100 2.698 2.688 2.689 2.103 1.994 1.988 95.8 93.8 95.1
0.85 20 2.803 2.823 2.795 2.802 9.810 9.444 9.313 94.0 94.2 95.7
100 2.814 2.802 2.803 2.147 1.947 1.942 95.9 94.0 94.5
0.90 20 2.934 2.956 2.925 2.932 9.907 9.175 9.037 94.0 94.4 95.2
100 2.947 2.933 2.934 2.204 1.890 1.886 96.0 93.8 94.0
0.95 20 3.105 3.131 3.095 3.102 10.112 8.826 8.684 94.1 94.1 94.7
100 3.123 3.104 3.105 2.335 1.812 1.808 96.5 94.1 93.6

Simulation results. log(κp) refers to the actual log-transformed Total Deviation Index (TDI) simulated, whereas Mean and MSE correspond to the mean value and mean squared error of the log-transformed TDI estimates from each of the scenarios considered, based on Lin, Choudhary and our Probability Interval (PI) approaches respectively. EC refers to the empirical confidence based on the 95% confidence level based on Lin, Choudhary (Ch.) and our Tolerance Interval (TI) upper bounds of the log-transformed TDI estimates respectively.