Table 1 Numerical values of simulation measures for \(\alpha =1.5,~\beta =2.0\) under SRS.
n | Est. | MLE | ADE | CVME | MPSE | OLSE | PCE | RTADE | WLSE |
|---|---|---|---|---|---|---|---|---|---|
30 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.18479 ^{\{ 3 \}}\) | \(0.18728 ^{\{ 5 \}}\) | \(0.21544 ^{\{ 10 \}}\) | \(0.18632 ^{\{ 4 \}}\) | \(0.21395 ^{\{ 9 \}}\) | \(0.18309 ^{\{ 1 \}}\) | \(0.20395 ^{\{ 7 \}}\) | \(0.19828 ^{\{ 6 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.22715 ^{\{ 6 \}}\) | \(0.21732 ^{\{ 3 \}}\) | \(0.23994 ^{\{ 11 \}}\) | \(0.20555 ^{\{ 1 \}}\) | \(0.22511 ^{\{ 5 \}}\) | \(0.20672 ^{\{ 2 \}}\) | \(0.23072 ^{\{ 7 \}}\) | \(0.21847 ^{\{ 4 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.06017 ^{\{ 5 \}}\) | \(0.05721 ^{\{ 4 \}}\) | \(0.08056 ^{\{ 10 \}}\) | \(0.0524 ^{\{ 2 \}}\) | \(0.07578 ^{\{ 9 \}}\) | \(0.04924 ^{\{ 1 \}}\) | \(0.07276 ^{\{ 8 \}}\) | \(0.06477 ^{\{ 6 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.08517 ^{\{ 6 \}}\) | \(0.07826 ^{\{ 4 \}}\) | \(0.09619 ^{\{ 12 \}}\) | \(0.06941 ^{\{ 2 \}}\) | \(0.08169 ^{\{ 5 \}}\) | \(0.06757 ^{\{ 1 \}}\) | \(0.08618 ^{\{ 7 \}}\) | \(0.07527 ^{\{ 3 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.12319 ^{\{ 3 \}}\) | \(0.12485 ^{\{ 5 \}}\) | \(0.14363 ^{\{ 10 \}}\) | \(0.12422 ^{\{ 4 \}}\) | \(0.14263 ^{\{ 9 \}}\) | \(0.12206 ^{\{ 1 \}}\) | \(0.13597 ^{\{ 7 \}}\) | \(0.13219 ^{\{ 6 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.11358 ^{\{ 6 \}}\) | \(0.10866 ^{\{ 3 \}}\) | \(0.11997 ^{\{ 11 \}}\) | \(0.10277 ^{\{ 1 \}}\) | \(0.11256 ^{\{ 5 \}}\) | \(0.10336 ^{\{ 2 \}}\) | \(0.11536 ^{\{ 7 \}}\) | \(0.10923 ^{\{ 4 \}}\) | |
\(\pmb K{_4}\) | \(0.04581 ^{\{ 1 \}}\) | \(0.04647 ^{\{ 2 \}}\) | \(0.0487 ^{\{ 6 \}}\) | \(0.0474 ^{\{ 3 \}}\) | \(0.04975 ^{\{ 8 \}}\) | \(0.04742 ^{\{ 4 \}}\) | \(0.04911 ^{\{ 7 \}}\) | \(0.04752 ^{\{ 5 \}}\) | |
\(\pmb K{_5}\) | \(0.0743 ^{\{ 2 \}}\) | \(0.07412 ^{\{ 1 \}}\) | \(0.08064 ^{\{ 9 \}}\) | \(0.07453 ^{\{ 3 \}}\) | \(0.08043 ^{\{ 8 \}}\) | \(0.0747 ^{\{ 4 \}}\) | \(0.07871 ^{\{ 6 \}}\) | \(0.07637 ^{\{ 5 \}}\) | |
ASAE | \(0.12151 ^{\{ 2 \}}\) | \(0.0922 ^{\{ 1 \}}\) | \(0.13371 ^{\{ 9 \}}\) | \(0.05709 ^{\{ 3 \}}\) | \(0.10566 ^{\{ 8 \}}\) | \(0.03195 ^{\{ 4 \}}\) | \(0.15187 ^{\{ 6 \}}\) | \(0.09768 ^{\{ 5 \}}\) | |
\(\sum Ranks\) | \(40 ^{\{ 4 \}}\) | \(31 ^{\{ 3 \}}\) | \(88 ^{\{ 10 \}}\) | \(22 ^{\{ 2 \}}\) | \(65 ^{\{ 7 \}}\) | \(17 ^{\{ 1 \}}\) | \(68 ^{\{ 8 \}}\) | \(44 ^{\{ 5 \}}\) | |
80 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.10593 ^{\{ 1 \}}\) | \(0.11489 ^{\{ 3 \}}\) | \(0.12647 ^{\{ 9 \}}\) | \(0.1085 ^{\{ 2 \}}\) | \(0.13351 ^{\{ 11 \}}\) | \(0.11617 ^{\{ 4 \}}\) | \(0.12228 ^{\{ 8 \}}\) | \(0.11647 ^{\{ 5 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.13479 ^{\{ 4 \}}\) | \(0.13585 ^{\{ 6 \}}\) | \(0.1419 ^{\{ 8 \}}\) | \(0.13158 ^{\{ 3 \}}\) | \(0.13562 ^{\{ 5 \}}\) | \(0.12736 ^{\{ 1 \}}\) | \(0.13768 ^{\{ 7 \}}\) | \(0.13133 ^{\{ 2 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.01809 ^{\{ 2 \}}\) | \(0.02161 ^{\{ 5 \}}\) | \(0.0257 ^{\{ 9 \}}\) | \(0.01734 ^{\{ 1 \}}\) | \(0.02852 ^{\{ 11 \}}\) | \(0.02061 ^{\{ 3 \}}\) | \(0.02416 ^{\{ 8 \}}\) | \(0.02173 ^{\{ 6 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.02981 ^{\{ 6 \}}\) | \(0.02863 ^{\{ 4 \}}\) | \(0.03182 ^{\{ 8 \}}\) | \(0.02755 ^{\{ 3 \}}\) | \(0.02936 ^{\{ 5 \}}\) | \(0.02597 ^{\{ 1 \}}\) | \(0.02997 ^{\{ 7 \}}\) | \(0.02746 ^{\{ 2 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.07062 ^{\{ 1 \}}\) | \(0.0766 ^{\{ 3 \}}\) | \(0.08431 ^{\{ 9 \}}\) | \(0.07233 ^{\{ 2 \}}\) | \(0.08901 ^{\{ 11 \}}\) | \(0.07745 ^{\{ 4 \}}\) | \(0.08152 ^{\{ 8 \}}\) | \(0.07764 ^{\{ 5 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.06739 ^{\{ 4 \}}\) | \(0.06793 ^{\{ 6 \}}\) | \(0.07095 ^{\{ 8 \}}\) | \(0.06579 ^{\{ 3 \}}\) | \(0.06781 ^{\{ 5 \}}\) | \(0.06368 ^{\{ 1 \}}\) | \(0.06884 ^{\{ 7 \}}\) | \(0.06567 ^{\{ 2 \}}\) | |
\(\pmb K{_4}\) | \(0.02811 ^{\{ 1 \}}\) | \(0.02899 ^{\{ 4 \}}\) | \(0.03027 ^{\{ 8 \}}\) | \(0.0292 ^{\{ 5 \}}\) | \(0.03006 ^{\{ 7 \}}\) | \(0.02852 ^{\{ 3 \}}\) | \(0.02958 ^{\{ 6 \}}\) | \(0.02824 ^{\{ 2 \}}\) | |
\(\pmb K{_5}\) | \(0.0449 ^{\{ 1 \}}\) | \(0.04657 ^{\{ 5 \}}\) | \(0.04948 ^{\{ 8 \}}\) | \(0.04618 ^{\{ 4 \}}\) | \(0.04927 ^{\{ 7 \}}\) | \(0.04548 ^{\{ 2 \}}\) | \(0.04756 ^{\{ 6 \}}\) | \(0.04575 ^{\{ 3 \}}\) | |
\(\pmb K{_6}\) | \(0.02132 ^{\{ 1 \}}\) | \(0.02182 ^{\{ 5 \}}\) | \(0.02255 ^{\{ 8 \}}\) | \(0.01898 ^{\{ 4 \}}\) | \(0.02734 ^{\{ 7 \}}\) | \(0.01827 ^{\{ 2 \}}\) | \(0.02539 ^{\{ 6 \}}\) | \(0.02317 ^{\{ 3 \}}\) | |
\(\sum Ranks\) | \(23 ^{\{ 2 \}}\) | \(40 ^{\{ 5 \}}\) | \(72 ^{\{ 7.5 \}}\) | \(25 ^{\{ 3 \}}\) | \(72 ^{\{ 7.5 \}}\) | \(20 ^{\{ 1 \}}\) | \(65 ^{\{ 6 \}}\) | \(33 ^{\{ 4 \}}\) | |
150 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.07561 ^{\{ 1 \}}\) | \(0.08112 ^{\{ 3 \}}\) | \(0.09827 ^{\{ 10 \}}\) | \(0.07599 ^{\{ 2 \}}\) | \(0.09268 ^{\{ 8 \}}\) | \(0.08348 ^{\{ 5 \}}\) | \(0.08685 ^{\{ 6 \}}\) | \(0.08144 ^{\{ 4 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.09492 ^{\{ 3 \}}\) | \(0.10085 ^{\{ 8 \}}\) | \(0.09895 ^{\{ 6 \}}\) | \(0.09537 ^{\{ 4 \}}\) | \(0.09737 ^{\{ 5 \}}\) | \(0.09401 ^{\{ 2 \}}\) | \(0.09395 ^{\{ 1 \}}\) | \(0.09904 ^{\{ 7 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00908 ^{\{ 2 \}}\) | \(0.01041 ^{\{ 3 \}}\) | \(0.01549 ^{\{ 11 \}}\) | \(0.00884 ^{\{ 1 \}}\) | \(0.01338 ^{\{ 9 \}}\) | \(0.01086 ^{\{ 5 \}}\) | \(0.01235 ^{\{ 7 \}}\) | \(0.01083 ^{\{ 4 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.01416 ^{\{ 1 \}}\) | \(0.01636 ^{\{ 9 \}}\) | \(0.01551 ^{\{ 6 \}}\) | \(0.01422 ^{\{ 2.5 \}}\) | \(0.01488 ^{\{ 5 \}}\) | \(0.01422 ^{\{ 2.5 \}}\) | \(0.01432 ^{\{ 4 \}}\) | \(0.01587 ^{\{ 7 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.05041 ^{\{ 1 \}}\) | \(0.05408 ^{\{ 3 \}}\) | \(0.06551 ^{\{ 10 \}}\) | \(0.05066 ^{\{ 2 \}}\) | \(0.06179 ^{\{ 8 \}}\) | \(0.05566 ^{\{ 5 \}}\) | \(0.0579 ^{\{ 6 \}}\) | \(0.05429 ^{\{ 4 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.04746 ^{\{ 3 \}}\) | \(0.05043 ^{\{ 8 \}}\) | \(0.04948 ^{\{ 6 \}}\) | \(0.04769 ^{\{ 4 \}}\) | \(0.04868 ^{\{ 5 \}}\) | \(0.047 ^{\{ 2 \}}\) | \(0.04697 ^{\{ 1 \}}\) | \(0.04952 ^{\{ 7 \}}\) | |
\(\pmb K{_4}\) | \(0.01989 ^{\{ 1 \}}\) | \(0.02121 ^{\{ 6 \}}\) | \(0.02172 ^{\{ 8 \}}\) | \(0.02051 ^{\{ 3 \}}\) | \(0.02135 ^{\{ 7 \}}\) | \(0.02072 ^{\{ 4 \}}\) | \(0.02046 ^{\{ 2 \}}\) | \(0.02101 ^{\{ 5 \}}\) | |
\(\pmb K{_5}\) | \(0.0319 ^{\{ 1 \}}\) | \(0.03415 ^{\{ 6 \}}\) | \(0.03588 ^{\{ 8 \}}\) | \(0.03275 ^{\{ 2 \}}\) | \(0.03497 ^{\{ 7 \}}\) | \(0.03319 ^{\{ 4 \}}\) | \(0.03316 ^{\{ 3 \}}\) | \(0.03392 ^{\{ 5 \}}\) | |
\(\pmb K{_6}\) | \(0.01315 ^{\{ 1 \}}\) | \(0.01252 ^{\{ 6 \}}\) | \(0.01394 ^{\{ 8 \}}\) | \(0.01303 ^{\{ 2 \}}\) | \(0.0129 ^{\{ 7 \}}\) | \(0.01258 ^{\{ 4 \}}\) | \(0.01279 ^{\{ 3 \}}\) | \(0.0125 ^{\{ 5 \}}\) | |
\(\sum Ranks\) | \(20 ^{\{ 1 \}}\) | \(48 ^{\{ 6 \}}\) | \(73 ^{\{ 8 \}}\) | \(26.5 ^{\{ 2 \}}\) | \(59 ^{\{ 7 \}}\) | \(32.5 ^{\{ 3 \}}\) | \(34 ^{\{ 4 \}}\) | \(44 ^{\{ 5 \}}\) | |
300 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.05593 ^{\{ 2 \}}\) | \(0.05634 ^{\{ 3 \}}\) | \(0.06461 ^{\{ 9 \}}\) | \(0.05539 ^{\{ 1 \}}\) | \(0.06515 ^{\{ 10 \}}\) | \(0.05843 ^{\{ 5 \}}\) | \(0.06174 ^{\{ 7 \}}\) | \(0.05899 ^{\{ 6 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.07155 ^{\{ 7 \}}\) | \(0.0669 ^{\{ 1 \}}\) | \(0.07197 ^{\{ 8 \}}\) | \(0.06829 ^{\{ 3 \}}\) | \(0.07141 ^{\{ 6 \}}\) | \(0.06731 ^{\{ 2 \}}\) | \(0.07053 ^{\{ 4 \}}\) | \(0.07059 ^{\{ 5 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00493 ^{\{ 2.5 \}}\) | \(0.00493 ^{\{ 2.5 \}}\) | \(0.0065 ^{\{ 9 \}}\) | \(0.00481 ^{\{ 1 \}}\) | \(0.0069 ^{\{ 10 \}}\) | \(0.00532 ^{\{ 5 \}}\) | \(0.00588 ^{\{ 7 \}}\) | \(0.00561 ^{\{ 6 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00799 ^{\{ 6 \}}\) | \(0.00721 ^{\{ 2 \}}\) | \(0.0082 ^{\{ 7 \}}\) | \(0.0072 ^{\{ 1 \}}\) | \(0.00825 ^{\{ 8 \}}\) | \(0.00728 ^{\{ 3 \}}\) | \(0.00759 ^{\{ 4 \}}\) | \(0.00794 ^{\{ 5 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.03728 ^{\{ 2 \}}\) | \(0.03756 ^{\{ 3 \}}\) | \(0.04308 ^{\{ 9 \}}\) | \(0.03693 ^{\{ 1 \}}\) | \(0.04343 ^{\{ 10 \}}\) | \(0.03896 ^{\{ 5 \}}\) | \(0.04116 ^{\{ 7 \}}\) | \(0.03933 ^{\{ 6 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.03578 ^{\{ 7 \}}\) | \(0.03345 ^{\{ 1 \}}\) | \(0.03598 ^{\{ 8 \}}\) | \(0.03415 ^{\{ 3 \}}\) | \(0.03571 ^{\{ 6 \}}\) | \(0.03365 ^{\{ 2 \}}\) | \(0.03526 ^{\{ 4 \}}\) | \(0.0353 ^{\{ 5 \}}\) | |
\(\pmb K{_4}\) | \(0.01496 ^{\{ 4 \}}\) | \(0.01435 ^{\{ 1 \}}\) | \(0.01554 ^{\{ 7 \}}\) | \(0.01458 ^{\{ 2 \}}\) | \(0.01567 ^{\{ 8 \}}\) | \(0.01468 ^{\{ 3 \}}\) | \(0.01517 ^{\{ 6 \}}\) | \(0.01504 ^{\{ 5 \}}\) | |
\(\pmb K{_5}\) | \(0.02389 ^{\{ 4 \}}\) | \(0.0231 ^{\{ 1 \}}\) | \(0.02532 ^{\{ 8 \}}\) | \(0.02329 ^{\{ 2 \}}\) | \(0.02548 ^{\{ 9 \}}\) | \(0.02353 ^{\{ 3 \}}\) | \(0.02448 ^{\{ 6 \}}\) | \(0.02426 ^{\{ 5 \}}\) | |
\(\pmb K{_6}\) | \(0.00863 ^{\{ 4 \}}\) | \(0.00833 ^{\{ 1 \}}\) | \(0.00851 ^{\{ 8 \}}\) | \(0.00865 ^{\{ 2 \}}\) | \(0.00857 ^{\{ 9 \}}\) | \(0.00852 ^{\{ 3 \}}\) | \(0.00825 ^{\{ 6 \}}\) | \(0.00828 ^{\{ 5 \}}\) | |
\(\sum Ranks\) | \(41.5 ^{\{ 4 \}}\) | \(17.5 ^{\{ 1 \}}\) | \(69 ^{\{ 8 \}}\) | \(22 ^{\{ 2 \}}\) | \(73 ^{\{ 9 \}}\) | \(33 ^{\{ 3 \}}\) | \(46 ^{\{ 6 \}}\) | \(45 ^{\{ 5 \}}\) |
400 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.04534 ^{\{ 1 \}}\) | \(0.05033 ^{\{ 5 \}}\) | \(0.05646 ^{\{ 9 \}}\) | \(0.04601 ^{\{ 2 \}}\) | \(0.05788 ^{\{ 10 \}}\) | \(0.05027 ^{\{ 4 \}}\) | \(0.05275 ^{\{ 6 \}}\) | \(0.04983 ^{\{ 3 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.06074 ^{\{ 4 \}}\) | \(0.06194 ^{\{ 9 \}}\) | \(0.06052 ^{\{ 3 \}}\) | \(0.05861 ^{\{ 2 \}}\) | \(0.06381 ^{\{ 10 \}}\) | \(0.05825 ^{\{ 1 \}}\) | \(0.06106 ^{\{ 6 \}}\) | \(0.0618 ^{\{ 7 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00329 ^{\{ 1 \}}\) | \(0.00391 ^{\{ 5 \}}\) | \(0.00503 ^{\{ 9 \}}\) | \(0.00331 ^{\{ 2 \}}\) | \(0.00523 ^{\{ 10 \}}\) | \(0.0039 ^{\{ 4 \}}\) | \(0.00444 ^{\{ 7 \}}\) | \(0.00382 ^{\{ 3 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.0058 ^{\{ 3 \}}\) | \(0.00602 ^{\{ 7 \}}\) | \(0.00584 ^{\{ 4 \}}\) | \(0.00544 ^{\{ 2 \}}\) | \(0.00626 ^{\{ 10 \}}\) | \(0.00531 ^{\{ 1 \}}\) | \(0.00596 ^{\{ 6 \}}\) | \(0.00613 ^{\{ 9 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.03022 ^{\{ 1 \}}\) | \(0.03355 ^{\{ 5 \}}\) | \(0.03764 ^{\{ 9 \}}\) | \(0.03068 ^{\{ 2 \}}\) | \(0.03859 ^{\{ 10 \}}\) | \(0.03352 ^{\{ 4 \}}\) | \(0.03516 ^{\{ 6 \}}\) | \(0.03322 ^{\{ 3 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.03037 ^{\{ 4 \}}\) | \(0.03097 ^{\{ 9 \}}\) | \(0.03026 ^{\{ 3 \}}\) | \(0.02931 ^{\{ 2 \}}\) | \(0.03191 ^{\{ 10 \}}\) | \(0.02912 ^{\{ 1 \}}\) | \(0.03053 ^{\{ 6 \}}\) | \(0.0309 ^{\{ 7 \}}\) | |
\(\pmb K{_4}\) | \(0.0126 ^{\{ 1.5 \}}\) | \(0.01311 ^{\{ 4.5 \}}\) | \(0.01327 ^{\{ 7 \}}\) | \(0.0126 ^{\{ 1.5 \}}\) | \(0.01386 ^{\{ 10 \}}\) | \(0.01271 ^{\{ 3 \}}\) | \(0.01318 ^{\{ 6 \}}\) | \(0.01311 ^{\{ 4.5 \}}\) | |
\(\pmb K{_5}\) | \(0.0201 ^{\{ 2 \}}\) | \(0.02109 ^{\{ 5 \}}\) | \(0.02163 ^{\{ 7 \}}\) | \(0.02002 ^{\{ 1 \}}\) | \(0.02258 ^{\{ 10 \}}\) | \(0.02027 ^{\{ 3 \}}\) | \(0.02112 ^{\{ 6 \}}\) | \(0.02107 ^{\{ 4 \}}\) | |
\(\pmb K{_6}\) | \(0.00739 ^{\{ 2 \}}\) | \(0.00694 ^{\{ 5 \}}\) | \(0.00719 ^{\{ 7 \}}\) | \(0.00736 ^{\{ 1 \}}\) | \(0.00727 ^{\{ 10 \}}\) | \(0.00722 ^{\{ 3 \}}\) | \(0.00696 ^{\{ 6 \}}\) | \(0.00705 ^{\{ 4 \}}\) | |
\(\sum Ranks\) | \(25.5 ^{\{ 2 \}}\) | \(50.5 ^{\{ 5 \}}\) | \(55 ^{\{ 7 \}}\) | \(21.5 ^{\{ 1 \}}\) | \(86 ^{\{ 9.5 \}}\) | \(26 ^{\{ 3 \}}\) | \(51 ^{\{ 6 \}}\) | \(43.5 ^{\{ 4 \}}\) | |
500 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.04129 ^{\{ 1 \}}\) | \(0.0467 ^{\{ 5 \}}\) | \(0.05101 ^{\{ 9 \}}\) | \(0.04306 ^{\{ 2 \}}\) | \(0.05228 ^{\{ 11 \}}\) | \(0.04705 ^{\{ 7 \}}\) | \(0.04701 ^{\{ 6 \}}\) | \(0.04612 ^{\{ 4 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.05165 ^{\{ 1 \}}\) | \(0.05205 ^{\{ 2 \}}\) | \(0.05635 ^{\{ 8 \}}\) | \(0.05244 ^{\{ 3 \}}\) | \(0.0554 ^{\{ 7 \}}\) | \(0.05268 ^{\{ 4 \}}\) | \(0.05388 ^{\{ 5 \}}\) | \(0.05503 ^{\{ 6 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00266 ^{\{ 1 \}}\) | \(0.00344 ^{\{ 5 \}}\) | \(0.00414 ^{\{ 9 \}}\) | \(0.00289 ^{\{ 2 \}}\) | \(0.0042 ^{\{ 10 \}}\) | \(0.00346 ^{\{ 6 \}}\) | \(0.00356 ^{\{ 7 \}}\) | \(0.00331 ^{\{ 3 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00418 ^{\{ 1 \}}\) | \(0.00429 ^{\{ 3 \}}\) | \(0.00497 ^{\{ 8 \}}\) | \(0.00428 ^{\{ 2 \}}\) | \(0.00469 ^{\{ 6 \}}\) | \(0.00433 ^{\{ 4 \}}\) | \(0.00462 ^{\{ 5 \}}\) | \(0.00485 ^{\{ 7 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.02752 ^{\{ 1 \}}\) | \(0.03114 ^{\{ 5 \}}\) | \(0.03401 ^{\{ 9 \}}\) | \(0.0287 ^{\{ 2 \}}\) | \(0.03485 ^{\{ 11 \}}\) | \(0.03136 ^{\{ 7 \}}\) | \(0.03134 ^{\{ 6 \}}\) | \(0.03075 ^{\{ 4 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.02583 ^{\{ 1 \}}\) | \(0.02603 ^{\{ 2 \}}\) | \(0.02817 ^{\{ 8 \}}\) | \(0.02622 ^{\{ 3 \}}\) | \(0.0277 ^{\{ 7 \}}\) | \(0.02634 ^{\{ 4 \}}\) | \(0.02694 ^{\{ 5 \}}\) | \(0.02752 ^{\{ 6 \}}\) | |
\(\pmb K{_4}\) | \(0.01083 ^{\{ 1 \}}\) | \(0.01128 ^{\{ 3 \}}\) | \(0.01217 ^{\{ 7 \}}\) | \(0.01118 ^{\{ 2 \}}\) | \(0.01219 ^{\{ 8 \}}\) | \(0.0115 ^{\{ 4 \}}\) | \(0.01159 ^{\{ 5 \}}\) | \(0.01175 ^{\{ 6 \}}\) | |
\(\pmb K{_5}\) | \(0.01745 ^{\{ 1 \}}\) | \(0.0183 ^{\{ 3 \}}\) | \(0.01982 ^{\{ 8 \}}\) | \(0.018 ^{\{ 2 \}}\) | \(0.01988 ^{\{ 9 \}}\) | \(0.01851 ^{\{ 4 \}}\) | \(0.01865 ^{\{ 5 \}}\) | \(0.0189 ^{\{ 6 \}}\) | |
\(\pmb K{_6}\) | \(0.0064 ^{\{ 1 \}}\) | \(0.0062 ^{\{ 3 \}}\) | \(0.00636 ^{\{ 8 \}}\) | \(0.00651 ^{\{ 2 \}}\) | \(0.00633 ^{\{ 9 \}}\) | \(0.00636 ^{\{ 4 \}}\) | \(0.00608 ^{\{ 5 \}}\) | \(0.00619 ^{\{ 6 \}}\) | |
\(\sum Ranks\) | \(15 ^{\{ 1 \}}\) | \(31 ^{\{ 3 \}}\) | \(72 ^{\{ 8 \}}\) | \(26 ^{\{ 2 \}}\) | \(73 ^{\{ 9 \}}\) | \(45 ^{\{ 5.5 \}}\) | \(45 ^{\{ 5.5 \}}\) | \(44 ^{\{ 4 \}}\) |
n | Est. | LTADE | MSADE | MSALDE | ADSOE | KE | MSSD | MSSLD | MSLND |
|---|---|---|---|---|---|---|---|---|---|
30 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.23108 ^{\{ 12 \}}\) | \(0.22584 ^{\{ 11 \}}\) | \(0.21019 ^{\{ 8 \}}\) | \(0.30305 ^{\{ 16 \}}\) | \(0.23705 ^{\{ 13 \}}\) | \(0.26207 ^{\{ 15 \}}\) | \(0.18452 ^{\{ 2 \}}\) | \(0.26054 ^{\{ 14 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.23705 ^{\{ 9 \}}\) | \(0.25263 ^{\{ 14 \}}\) | \(0.23621 ^{\{ 8 \}}\) | \(0.29631 ^{\{ 16 \}}\) | \(0.24103 ^{\{ 12 \}}\) | \(0.24433 ^{\{ 13 \}}\) | \(0.23808 ^{\{ 10 \}}\) | \(0.25935 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.09243 ^{\{ 12 \}}\) | \(0.08592 ^{\{ 11 \}}\) | \(0.06732 ^{\{ 7 \}}\) | \(0.15065 ^{\{ 16 \}}\) | \(0.09792 ^{\{ 13 \}}\) | \(0.10894 ^{\{ 15 \}}\) | \(0.05275 ^{\{ 3 \}}\) | \(0.10281 ^{\{ 14 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.09275 ^{\{ 10 \}}\) | \(0.10189 ^{\{ 14 \}}\) | \(0.08786 ^{\{ 8 \}}\) | \(0.17315 ^{\{ 16 \}}\) | \(0.09539 ^{\{ 11 \}}\) | \(0.09905 ^{\{ 13 \}}\) | \(0.08831 ^{\{ 9 \}}\) | \(0.11359 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.15405 ^{\{ 12 \}}\) | \(0.15056 ^{\{ 11 \}}\) | \(0.14013 ^{\{ 8 \}}\) | \(0.20203 ^{\{ 16 \}}\) | \(0.15803 ^{\{ 13 \}}\) | \(0.17472 ^{\{ 15 \}}\) | \(0.12301 ^{\{ 2 \}}\) | \(0.17369 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.11852 ^{\{ 9 \}}\) | \(0.12631 ^{\{ 14 \}}\) | \(0.11811 ^{\{ 8 \}}\) | \(0.14816 ^{\{ 16 \}}\) | \(0.12052 ^{\{ 12 \}}\) | \(0.12217 ^{\{ 13 \}}\) | \(0.11904 ^{\{ 10 \}}\) | \(0.12967 ^{\{ 15 \}}\) | |
\(\pmb K{_4}\) | \(0.05021 ^{\{ 10 \}}\) | \(0.05522 ^{\{ 13 \}}\) | \(0.05383 ^{\{ 12 \}}\) | \(0.05853 ^{\{ 14 \}}\) | \(0.04991 ^{\{ 9 \}}\) | \(0.05946 ^{\{ 15 \}}\) | \(0.05076 ^{\{ 11 \}}\) | \(0.06175 ^{\{ 16 \}}\) | |
\(\pmb K{_5}\) | \(0.08281 ^{\{ 10 \}}\) | \(0.08824 ^{\{ 13 \}}\) | \(0.08483 ^{\{ 12 \}}\) | \(0.10292 ^{\{ 16 \}}\) | \(0.08307 ^{\{ 11 \}}\) | \(0.09612 ^{\{ 14 \}}\) | \(0.07995 ^{\{ 7 \}}\) | \(0.09888 ^{\{ 15 \}}\) | |
ASAE | \(0.15303 ^{\{ 10 \}}\) | \(0.15103 ^{\{ 13 \}}\) | \(0.0984 ^{\{ 12 \}}\) | \(0.20278 ^{\{ 16 \}}\) | \(0.18754 ^{\{ 11 \}}\) | \(0.1809 ^{\{ 14 \}}\) | \(0.07469 ^{\{ 7 \}}\) | \(0.13518 ^{\{ 15 \}}\) | |
\(\sum Ranks\) | \(97 ^{\{ 11 \}}\) | \(112 ^{\{ 13 \}}\) | \(77 ^{\{ 9 \}}\) | \(142 ^{\{ 16 \}}\) | \(109 ^{\{ 12 \}}\) | \(127 ^{\{ 14 \}}\) | \(57 ^{\{ 6 \}}\) | \(128 ^{\{ 15 \}}\) | |
80 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.14208 ^{\{ 13 \}}\) | \(0.13891 ^{\{ 12 \}}\) | \(0.11963 ^{\{ 7 \}}\) | \(0.18948 ^{\{ 16 \}}\) | \(0.13075 ^{\{ 10 \}}\) | \(0.15731 ^{\{ 15 \}}\) | \(0.1167 ^{\{ 6 \}}\) | \(0.15575 ^{\{ 14 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.14413 ^{\{ 9 \}}\) | \(0.16552 ^{\{ 13 \}}\) | \(0.15468 ^{\{ 12 \}}\) | \(0.17808 ^{\{ 16 \}}\) | \(0.14447 ^{\{ 10 \}}\) | \(0.16965 ^{\{ 14 \}}\) | \(0.14786 ^{\{ 11 \}}\) | \(0.17086 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.03221 ^{\{ 13 \}}\) | \(0.02953 ^{\{ 12 \}}\) | \(0.0224 ^{\{ 7 \}}\) | \(0.0586 ^{\{ 16 \}}\) | \(0.02826 ^{\{ 10 \}}\) | \(0.0392 ^{\{ 14 \}}\) | \(0.02143 ^{\{ 4 \}}\) | \(0.03998 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.03347 ^{\{ 10 \}}\) | \(0.04311 ^{\{ 13 \}}\) | \(0.03713 ^{\{ 12 \}}\) | \(0.05385 ^{\{ 16 \}}\) | \(0.03252 ^{\{ 9 \}}\) | \(0.04879 ^{\{ 15 \}}\) | \(0.03436 ^{\{ 11 \}}\) | \(0.04803 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.09472 ^{\{ 13 \}}\) | \(0.0926 ^{\{ 12 \}}\) | \(0.07976 ^{\{ 7 \}}\) | \(0.12632 ^{\{ 16 \}}\) | \(0.08717 ^{\{ 10 \}}\) | \(0.10488 ^{\{ 15 \}}\) | \(0.0778 ^{\{ 6 \}}\) | \(0.10383 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.07207 ^{\{ 9 \}}\) | \(0.08276 ^{\{ 13 \}}\) | \(0.07734 ^{\{ 12 \}}\) | \(0.08904 ^{\{ 16 \}}\) | \(0.07224 ^{\{ 10 \}}\) | \(0.08483 ^{\{ 14 \}}\) | \(0.07393 ^{\{ 11 \}}\) | \(0.08543 ^{\{ 15 \}}\) | |
\(\pmb K{_4}\) | \(0.0311 ^{\{ 10 \}}\) | \(0.0358 ^{\{ 13 \}}\) | \(0.03336 ^{\{ 12 \}}\) | \(0.03838 ^{\{ 16 \}}\) | \(0.03042 ^{\{ 9 \}}\) | \(0.03807 ^{\{ 14 \}}\) | \(0.03147 ^{\{ 11 \}}\) | \(0.03831 ^{\{ 15 \}}\) | |
\(\pmb K{_5}\) | \(0.05156 ^{\{ 11 \}}\) | \(0.0573 ^{\{ 13 \}}\) | \(0.05282 ^{\{ 12 \}}\) | \(0.06802 ^{\{ 16 \}}\) | \(0.05018 ^{\{ 10 \}}\) | \(0.06158 ^{\{ 14 \}}\) | \(0.04979 ^{\{ 9 \}}\) | \(0.0617 ^{\{ 15 \}}\) | |
\(\pmb K{_6}\) | \(0.0286 ^{\{ 11 \}}\) | \(0.03434 ^{\{ 13 \}}\) | \(0.02529 ^{\{ 12 \}}\) | \(0.04978 ^{\{ 16 \}}\) | \(0.02918 ^{\{ 10 \}}\) | \(0.04443 ^{\{ 14 \}}\) | \(0.02621 ^{\{ 9 \}}\) | \(0.0486 ^{\{ 15 \}}\) | |
\(\sum Ranks\) | \(99 ^{\{ 12 \}}\) | \(114 ^{\{ 13 \}}\) | \(88 ^{\{ 10 \}}\) | \(144 ^{\{ 16 \}}\) | \(90 ^{\{ 11 \}}\) | \(129 ^{\{ 14 \}}\) | \(78 ^{\{ 9 \}}\) | \(132 ^{\{ 15 \}}\) | |
150 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.09918 ^{\{ 11 \}}\) | \(0.09993 ^{\{ 12 \}}\) | \(0.09316 ^{\{ 9 \}}\) | \(0.13902 ^{\{ 16 \}}\) | \(0.1014 ^{\{ 13 \}}\) | \(0.1117 ^{\{ 14 \}}\) | \(0.08767 ^{\{ 7 \}}\) | \(0.11525 ^{\{ 15 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.10215 ^{\{ 9 \}}\) | \(0.11284 ^{\{ 13 \}}\) | \(0.11114 ^{\{ 12 \}}\) | \(0.1326 ^{\{ 16 \}}\) | \(0.10678 ^{\{ 10 \}}\) | \(0.128 ^{\{ 15 \}}\) | \(0.10803 ^{\{ 11 \}}\) | \(0.12307 ^{\{ 14 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.01527 ^{\{ 10 \}}\) | \(0.01641 ^{\{ 12 \}}\) | \(0.01317 ^{\{ 8 \}}\) | \(0.03249 ^{\{ 16 \}}\) | \(0.01676 ^{\{ 13 \}}\) | \(0.01932 ^{\{ 14 \}}\) | \(0.01185 ^{\{ 6 \}}\) | \(0.02093 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.01628 ^{\{ 8 \}}\) | \(0.02054 ^{\{ 13 \}}\) | \(0.02 ^{\{ 12 \}}\) | \(0.02863 ^{\{ 16 \}}\) | \(0.01785 ^{\{ 10 \}}\) | \(0.02568 ^{\{ 15 \}}\) | \(0.01844 ^{\{ 11 \}}\) | \(0.02418 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.06612 ^{\{ 11 \}}\) | \(0.06662 ^{\{ 12 \}}\) | \(0.06211 ^{\{ 9 \}}\) | \(0.09268 ^{\{ 16 \}}\) | \(0.0676 ^{\{ 13 \}}\) | \(0.07447 ^{\{ 14 \}}\) | \(0.05845 ^{\{ 7 \}}\) | \(0.07683 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.05107 ^{\{ 9 \}}\) | \(0.05642 ^{\{ 13 \}}\) | \(0.05557 ^{\{ 12 \}}\) | \(0.0663 ^{\{ 16 \}}\) | \(0.05339 ^{\{ 10 \}}\) | \(0.064 ^{\{ 15 \}}\) | \(0.05402 ^{\{ 11 \}}\) | \(0.06153 ^{\{ 14 \}}\) | |
\(\pmb K{_4}\) | \(0.02202 ^{\{ 9 \}}\) | \(0.02456 ^{\{ 13 \}}\) | \(0.02413 ^{\{ 12 \}}\) | \(0.02917 ^{\{ 16 \}}\) | \(0.02313 ^{\{ 10 \}}\) | \(0.02809 ^{\{ 15 \}}\) | \(0.02323 ^{\{ 11 \}}\) | \(0.02751 ^{\{ 14 \}}\) | |
\(\pmb K{_5}\) | \(0.03684 ^{\{ 9 \}}\) | \(0.03972 ^{\{ 13 \}}\) | \(0.03858 ^{\{ 12 \}}\) | \(0.05123 ^{\{ 16 \}}\) | \(0.03816 ^{\{ 11 \}}\) | \(0.04529 ^{\{ 15 \}}\) | \(0.03696 ^{\{ 10 \}}\) | \(0.04455 ^{\{ 14 \}}\) | |
\(\pmb K{_6}\) | \(0.01438 ^{\{ 9 \}}\) | \(0.02029 ^{\{ 13 \}}\) | \(0.01684 ^{\{ 12 \}}\) | \(0.0284 ^{\{ 16 \}}\) | \(0.0154 ^{\{ 11 \}}\) | \(0.02113 ^{\{ 15 \}}\) | \(0.01617 ^{\{ 10 \}}\) | \(0.0216 ^{\{ 14 \}}\) | |
\(\sum Ranks\) | \(85 ^{\{ 9.5 \}}\) | \(114 ^{\{ 13 \}}\) | \(98 ^{\{ 11 \}}\) | \(144 ^{\{ 16 \}}\) | \(100 ^{\{ 12 \}}\) | \(131 ^{\{ 15 \}}\) | \(85 ^{\{ 9.5 \}}\) | \(130 ^{\{ 14 \}}\) | |
300 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.06559 ^{\{ 11 \}}\) | \(0.06909 ^{\{ 13 \}}\) | \(0.06295 ^{\{ 8 \}}\) | \(0.1108 ^{\{ 16 \}}\) | \(0.06835 ^{\{ 12 \}}\) | \(0.07748 ^{\{ 14 \}}\) | \(0.05778 ^{\{ 4 \}}\) | \(0.07834 ^{\{ 15 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.07434 ^{\{ 11 \}}\) | \(0.08683 ^{\{ 13 \}}\) | \(0.08068 ^{\{ 12 \}}\) | \(0.09814 ^{\{ 16 \}}\) | \(0.07398 ^{\{ 10 \}}\) | \(0.09065 ^{\{ 14 \}}\) | \(0.07352 ^{\{ 9 \}}\) | \(0.0908 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00704 ^{\{ 11 \}}\) | \(0.00755 ^{\{ 13 \}}\) | \(0.00621 ^{\{ 8 \}}\) | \(0.01986 ^{\{ 16 \}}\) | \(0.00723 ^{\{ 12 \}}\) | \(0.00966 ^{\{ 14 \}}\) | \(0.00522 ^{\{ 4 \}}\) | \(0.00981 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00875 ^{\{ 11 \}}\) | \(0.01203 ^{\{ 13 \}}\) | \(0.00999 ^{\{ 12 \}}\) | \(0.01525 ^{\{ 16 \}}\) | \(0.00849 ^{\{ 10 \}}\) | \(0.01296 ^{\{ 15 \}}\) | \(0.00846 ^{\{ 9 \}}\) | \(0.01283 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.04372 ^{\{ 11 \}}\) | \(0.04606 ^{\{ 13 \}}\) | \(0.04196 ^{\{ 8 \}}\) | \(0.07387 ^{\{ 16 \}}\) | \(0.04557 ^{\{ 12 \}}\) | \(0.05165 ^{\{ 14 \}}\) | \(0.03852 ^{\{ 4 \}}\) | \(0.05223 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.03717 ^{\{ 11 \}}\) | \(0.04342 ^{\{ 13 \}}\) | \(0.04034 ^{\{ 12 \}}\) | \(0.04907 ^{\{ 16 \}}\) | \(0.03699 ^{\{ 10 \}}\) | \(0.04532 ^{\{ 14 \}}\) | \(0.03676 ^{\{ 9 \}}\) | \(0.0454 ^{\{ 15 \}}\) | |
\(\pmb K{_4}\) | \(0.01603 ^{\{ 10 \}}\) | \(0.01835 ^{\{ 13 \}}\) | \(0.01729 ^{\{ 12 \}}\) | \(0.0218 ^{\{ 16 \}}\) | \(0.01613 ^{\{ 11 \}}\) | \(0.01985 ^{\{ 14 \}}\) | \(0.0157 ^{\{ 9 \}}\) | \(0.0199 ^{\{ 15 \}}\) | |
\(\pmb K{_5}\) | \(0.02629 ^{\{ 10 \}}\) | \(0.02943 ^{\{ 13 \}}\) | \(0.02754 ^{\{ 12 \}}\) | \(0.03905 ^{\{ 16 \}}\) | \(0.02637 ^{\{ 11 \}}\) | \(0.03188 ^{\{ 14 \}}\) | \(0.02504 ^{\{ 7 \}}\) | \(0.03204 ^{\{ 15 \}}\) | |
\(\pmb K{_6}\) | \(0.00955 ^{\{ 10 \}}\) | \(0.01197 ^{\{ 13 \}}\) | \(0.01115 ^{\{ 12 \}}\) | \(0.01828 ^{\{ 16 \}}\) | \(0.0093 ^{\{ 11 \}}\) | \(0.01323 ^{\{ 14 \}}\) | \(0.01035 ^{\{ 7 \}}\) | \(0.01355 ^{\{ 15 \}}\) | |
\(\sum Ranks\) | \(96 ^{\{ 10.5 \}}\) | \(117 ^{\{ 13 \}}\) | \(96 ^{\{ 10.5 \}}\) | \(144 ^{\{ 16 \}}\) | \(97 ^{\{ 12 \}}\) | \(127 ^{\{ 14 \}}\) | \(66 ^{\{ 7 \}}\) | \(134 ^{\{ 15 \}}\) |
400 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.05971 ^{\{ 11 \}}\) | \(0.0612 ^{\{ 13 \}}\) | \(0.05461 ^{\{ 8 \}}\) | \(0.09201 ^{\{ 16 \}}\) | \(0.05986 ^{\{ 12 \}}\) | \(0.06655 ^{\{ 15 \}}\) | \(0.05308 ^{\{ 7 \}}\) | \(0.06629 ^{\{ 14 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.0609 ^{\{ 5 \}}\) | \(0.07248 ^{\{ 13 \}}\) | \(0.07159 ^{\{ 12 \}}\) | \(0.08484 ^{\{ 16 \}}\) | \(0.06182 ^{\{ 8 \}}\) | \(0.07748 ^{\{ 14 \}}\) | \(0.06866 ^{\{ 11 \}}\) | \(0.08166 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00555 ^{\{ 11 \}}\) | \(0.00568 ^{\{ 12 \}}\) | \(0.00456 ^{\{ 8 \}}\) | \(0.01436 ^{\{ 16 \}}\) | \(0.00576 ^{\{ 13 \}}\) | \(0.00688 ^{\{ 15 \}}\) | \(0.00436 ^{\{ 6 \}}\) | \(0.00675 ^{\{ 14 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00593 ^{\{ 5 \}}\) | \(0.00832 ^{\{ 13 \}}\) | \(0.00796 ^{\{ 12 \}}\) | \(0.01143 ^{\{ 16 \}}\) | \(0.00611 ^{\{ 8 \}}\) | \(0.00957 ^{\{ 14 \}}\) | \(0.00739 ^{\{ 11 \}}\) | \(0.01023 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.03981 ^{\{ 11 \}}\) | \(0.0408 ^{\{ 13 \}}\) | \(0.03641 ^{\{ 8 \}}\) | \(0.06134 ^{\{ 16 \}}\) | \(0.03991 ^{\{ 12 \}}\) | \(0.04437 ^{\{ 15 \}}\) | \(0.03539 ^{\{ 7 \}}\) | \(0.04419 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.03045 ^{\{ 5 \}}\) | \(0.03624 ^{\{ 13 \}}\) | \(0.0358 ^{\{ 12 \}}\) | \(0.04242 ^{\{ 16 \}}\) | \(0.03091 ^{\{ 8 \}}\) | \(0.03874 ^{\{ 14 \}}\) | \(0.03433 ^{\{ 11 \}}\) | \(0.04083 ^{\{ 15 \}}\) | |
\(\pmb K{_4}\) | \(0.01338 ^{\{ 8 \}}\) | \(0.01565 ^{\{ 13 \}}\) | \(0.01514 ^{\{ 12 \}}\) | \(0.01874 ^{\{ 16 \}}\) | \(0.01367 ^{\{ 9 \}}\) | \(0.0169 ^{\{ 14 \}}\) | \(0.01448 ^{\{ 11 \}}\) | \(0.0176 ^{\{ 15 \}}\) | |
\(\pmb K{_5}\) | \(0.02228 ^{\{ 8 \}}\) | \(0.02504 ^{\{ 13 \}}\) | \(0.02413 ^{\{ 12 \}}\) | \(0.03347 ^{\{ 16 \}}\) | \(0.02237 ^{\{ 9 \}}\) | \(0.02721 ^{\{ 14 \}}\) | \(0.02312 ^{\{ 11 \}}\) | \(0.02817 ^{\{ 15 \}}\) | |
\(\pmb K{_6}\) | \(0.00807 ^{\{ 8 \}}\) | \(0.01018 ^{\{ 13 \}}\) | \(0.00947 ^{\{ 12 \}}\) | \(0.01509 ^{\{ 16 \}}\) | \(0.0078 ^{\{ 9 \}}\) | \(0.01131 ^{\{ 14 \}}\) | \(0.00889 ^{\{ 11 \}}\) | \(0.01133 ^{\{ 15 \}}\) | |
\(\sum Ranks\) | \(74 ^{\{ 8 \}}\) | \(116 ^{\{ 13 \}}\) | \(96 ^{\{ 12 \}}\) | \(144 ^{\{ 16 \}}\) | \(88 ^{\{ 11 \}}\) | \(129 ^{\{ 14 \}}\) | \(86 ^{\{ 9.5 \}}\) | \(132 ^{\{ 15 \}}\) | |
500 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.05189 ^{\{ 10 \}}\) | \(0.05244 ^{\{ 12 \}}\) | \(0.05098 ^{\{ 8 \}}\) | \(0.08797 ^{\{ 16 \}}\) | \(0.05261 ^{\{ 13 \}}\) | \(0.05864 ^{\{ 14 \}}\) | \(0.04603 ^{\{ 3 \}}\) | \(0.05977 ^{\{ 15 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.05674 ^{\{ 10 \}}\) | \(0.06384 ^{\{ 13 \}}\) | \(0.06241 ^{\{ 12 \}}\) | \(0.07671 ^{\{ 16 \}}\) | \(0.05655 ^{\{ 9 \}}\) | \(0.07096 ^{\{ 15 \}}\) | \(0.05775 ^{\{ 11 \}}\) | \(0.06872 ^{\{ 14 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00426 ^{\{ 11 \}}\) | \(0.00432 ^{\{ 12 \}}\) | \(0.00403 ^{\{ 8 \}}\) | \(0.0131 ^{\{ 16 \}}\) | \(0.00445 ^{\{ 13 \}}\) | \(0.00529 ^{\{ 14 \}}\) | \(0.00334 ^{\{ 4 \}}\) | \(0.00551 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00504 ^{\{ 9.5 \}}\) | \(0.0065 ^{\{ 13 \}}\) | \(0.00613 ^{\{ 12 \}}\) | \(0.00944 ^{\{ 16 \}}\) | \(0.00504 ^{\{ 9.5 \}}\) | \(0.00806 ^{\{ 15 \}}\) | \(0.00525 ^{\{ 11 \}}\) | \(0.00738 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.03459 ^{\{ 10 \}}\) | \(0.03496 ^{\{ 12 \}}\) | \(0.03399 ^{\{ 8 \}}\) | \(0.05865 ^{\{ 16 \}}\) | \(0.03507 ^{\{ 13 \}}\) | \(0.0391 ^{\{ 14 \}}\) | \(0.03069 ^{\{ 3 \}}\) | \(0.03985 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.02837 ^{\{ 10 \}}\) | \(0.03192 ^{\{ 13 \}}\) | \(0.03121 ^{\{ 12 \}}\) | \(0.03836 ^{\{ 16 \}}\) | \(0.02827 ^{\{ 9 \}}\) | \(0.03548 ^{\{ 15 \}}\) | \(0.02888 ^{\{ 11 \}}\) | \(0.03436 ^{\{ 14 \}}\) | |
\(\pmb K{_4}\) | \(0.01222 ^{\{ 9 \}}\) | \(0.01369 ^{\{ 13 \}}\) | \(0.01335 ^{\{ 12 \}}\) | \(0.01716 ^{\{ 16 \}}\) | \(0.0123 ^{\{ 11 \}}\) | \(0.01533 ^{\{ 15 \}}\) | \(0.01228 ^{\{ 10 \}}\) | \(0.01502 ^{\{ 14 \}}\) | |
\(\pmb K{_5}\) | \(0.02022 ^{\{ 10.5 \}}\) | \(0.02198 ^{\{ 13 \}}\) | \(0.02131 ^{\{ 12 \}}\) | \(0.0309 ^{\{ 16 \}}\) | \(0.02022 ^{\{ 10.5 \}}\) | \(0.02453 ^{\{ 15 \}}\) | \(0.01966 ^{\{ 7 \}}\) | \(0.02416 ^{\{ 14 \}}\) | |
\(\pmb K{_6}\) | \(0.00691 ^{\{ 10.5 \}}\) | \(0.00896 ^{\{ 13 \}}\) | \(0.00839 ^{\{ 12 \}}\) | \(0.0139 ^{\{ 16 \}}\) | \(0.00699 ^{\{ 10.5 \}}\) | \(0.00993 ^{\{ 15 \}}\) | \(0.0077 ^{\{ 7 \}}\) | \(0.00982 ^{\{ 14 \}}\) | |
\(\sum Ranks\) | \(89 ^{\{ 10 \}}\) | \(114 ^{\{ 13 \}}\) | \(96 ^{\{ 11 \}}\) | \(144 ^{\{ 16 \}}\) | \(98 ^{\{ 12 \}}\) | \(132 ^{\{ 15 \}}\) | \(71 ^{\{ 7 \}}\) | \(129 ^{\{ 14 \}}\) |
