Table 9 Numerical values of simulation measures for \(\alpha =0.9,~\beta =2.5\) under SRS.
n | Est. | MLE | ADE | CVME | MPSE | OLSE | PCE | RTADE | WLSE |
|---|---|---|---|---|---|---|---|---|---|
30 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.10608 ^{\{ 3 \}}\) | \(0.10182 ^{\{ 1 \}}\) | \(0.13814 ^{\{ 8 \}}\) | \(0.12037 ^{\{ 6 \}}\) | \(0.13912 ^{\{ 10 \}}\) | \(0.15341 ^{\{ 12 \}}\) | \(0.1036 ^{\{ 2 \}}\) | \(0.12296 ^{\{ 7 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.25391 ^{\{ 5 \}}\) | \(0.30736 ^{\{ 11 \}}\) | \(0.26074 ^{\{ 6 \}}\) | \(0.23677 ^{\{ 3 \}}\) | \(0.23656 ^{\{ 2 \}}\) | \(0.22259 ^{\{ 1 \}}\) | \(0.28984 ^{\{ 9 \}}\) | \(0.29083 ^{\{ 10 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.01857 ^{\{ 2 \}}\) | \(0.01708 ^{\{ 1 \}}\) | \(0.03471 ^{\{ 11 \}}\) | \(0.02236 ^{\{ 6 \}}\) | \(0.03001 ^{\{ 8 \}}\) | \(0.03678 ^{\{ 12 \}}\) | \(0.01898 ^{\{ 3 \}}\) | \(0.02603 ^{\{ 7 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.10943 ^{\{ 5 \}}\) | \(0.15305 ^{\{ 11 \}}\) | \(0.11365 ^{\{ 6 \}}\) | \(0.08887 ^{\{ 2 \}}\) | \(0.10033 ^{\{ 4 \}}\) | \(0.07581 ^{\{ 1 \}}\) | \(0.13434 ^{\{ 10 \}}\) | \(0.13374 ^{\{ 9 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.11787 ^{\{ 3 \}}\) | \(0.11313 ^{\{ 1 \}}\) | \(0.15349 ^{\{ 8 \}}\) | \(0.13375 ^{\{ 6 \}}\) | \(0.15458 ^{\{ 10 \}}\) | \(0.17046 ^{\{ 12 \}}\) | \(0.11511 ^{\{ 2 \}}\) | \(0.13662 ^{\{ 7 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.10157 ^{\{ 5 \}}\) | \(0.12294 ^{\{ 11 \}}\) | \(0.1043 ^{\{ 6 \}}\) | \(0.09471 ^{\{ 3 \}}\) | \(0.09462 ^{\{ 2 \}}\) | \(0.08903 ^{\{ 1 \}}\) | \(0.11593 ^{\{ 9 \}}\) | \(0.11633 ^{\{ 10 \}}\) | |
\(\pmb K{_4}\) | \(0.04368 ^{\{ 1 \}}\) | \(0.04841 ^{\{ 7 \}}\) | \(0.04529 ^{\{ 2 \}}\) | \(0.04658 ^{\{ 5 \}}\) | \(0.04562 ^{\{ 3 \}}\) | \(0.04944 ^{\{ 9 \}}\) | \(0.04836 ^{\{ 6 \}}\) | \(0.05033 ^{\{ 10 \}}\) | |
\(\pmb K{_5}\) | \(0.07057 ^{\{ 1 \}}\) | \(0.07594 ^{\{ 8 \}}\) | \(0.07436 ^{\{ 3 \}}\) | \(0.07519 ^{\{ 4 \}}\) | \(0.07534 ^{\{ 5 \}}\) | \(0.08111 ^{\{ 10 \}}\) | \(0.07564 ^{\{ 6 \}}\) | \(0.08091 ^{\{ 9 \}}\) | |
\(\pmb K{_6}\) | \(0.03443 ^{\{ 1 \}}\) | \(0.03316 ^{\{ 8 \}}\) | \(0.03478 ^{\{ 3 \}}\) | \(0.0316 ^{\{ 4 \}}\) | \(0.03345 ^{\{ 5 \}}\) | \(0.02938 ^{\{ 10 \}}\) | \(0.03102 ^{\{ 6 \}}\) | \(0.03152 ^{\{ 9 \}}\) | |
\(\sum Ranks\) | \(32 ^{\{ 1 \}}\) | \(56 ^{\{ 6 \}}\) | \(58 ^{\{ 7 \}}\) | \(39 ^{\{ 2 \}}\) | \(50 ^{\{ 5 \}}\) | \(59 ^{\{ 8 \}}\) | \(49 ^{\{ 4 \}}\) | \(72 ^{\{ 10 \}}\) | |
80 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.06617 ^{\{ 2 \}}\) | \(0.07039 ^{\{ 4 \}}\) | \(0.07998 ^{\{ 9 \}}\) | \(0.06564 ^{\{ 1 \}}\) | \(0.07969 ^{\{ 7 \}}\) | \(0.09965 ^{\{ 15 \}}\) | \(0.07981 ^{\{ 8 \}}\) | \(0.06999 ^{\{ 3 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.14858 ^{\{ 1 \}}\) | \(0.16162 ^{\{ 3 \}}\) | \(0.17484 ^{\{ 6 \}}\) | \(0.17248 ^{\{ 5 \}}\) | \(0.15808 ^{\{ 2 \}}\) | \(0.18935 ^{\{ 11 \}}\) | \(0.16313 ^{\{ 4 \}}\) | \(0.19112 ^{\{ 12 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00706 ^{\{ 2 \}}\) | \(0.0084 ^{\{ 5 \}}\) | \(0.0104 ^{\{ 8 \}}\) | \(0.00643 ^{\{ 1 \}}\) | \(0.00905 ^{\{ 7 \}}\) | \(0.01496 ^{\{ 15 \}}\) | \(0.01053 ^{\{ 10 \}}\) | \(0.00758 ^{\{ 3 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.03496 ^{\{ 1 \}}\) | \(0.03943 ^{\{ 2 \}}\) | \(0.0469 ^{\{ 6 \}}\) | \(0.04577 ^{\{ 5 \}}\) | \(0.04229 ^{\{ 4 \}}\) | \(0.05086 ^{\{ 9 \}}\) | \(0.04007 ^{\{ 3 \}}\) | \(0.05422 ^{\{ 11 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.07352 ^{\{ 2 \}}\) | \(0.07822 ^{\{ 4 \}}\) | \(0.08886 ^{\{ 9 \}}\) | \(0.07293 ^{\{ 1 \}}\) | \(0.08854 ^{\{ 7 \}}\) | \(0.11072 ^{\{ 15 \}}\) | \(0.08868 ^{\{ 8 \}}\) | \(0.07777 ^{\{ 3 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.05943 ^{\{ 1 \}}\) | \(0.06465 ^{\{ 3 \}}\) | \(0.06994 ^{\{ 6 \}}\) | \(0.06899 ^{\{ 5 \}}\) | \(0.06323 ^{\{ 2 \}}\) | \(0.07574 ^{\{ 11 \}}\) | \(0.06525 ^{\{ 4 \}}\) | \(0.07645 ^{\{ 12 \}}\) | |
\(\pmb K{_4}\) | \(0.02512 ^{\{ 1 \}}\) | \(0.02869 ^{\{ 3 \}}\) | \(0.02967 ^{\{ 5 \}}\) | \(0.03015 ^{\{ 7 \}}\) | \(0.02826 ^{\{ 2 \}}\) | \(0.03868 ^{\{ 16 \}}\) | \(0.02974 ^{\{ 6 \}}\) | \(0.03218 ^{\{ 9 \}}\) | |
\(\pmb K{_5}\) | \(0.04055 ^{\{ 1 \}}\) | \(0.04599 ^{\{ 2 \}}\) | \(0.04811 ^{\{ 6 \}}\) | \(0.04763 ^{\{ 4 \}}\) | \(0.04624 ^{\{ 3 \}}\) | \(0.06065 ^{\{ 14 \}}\) | \(0.04782 ^{\{ 5 \}}\) | \(0.05093 ^{\{ 8 \}}\) | |
\(\pmb K{_6}\) | \(0.01791 ^{\{ 1 \}}\) | \(0.0173 ^{\{ 2 \}}\) | \(0.01875 ^{\{ 6 \}}\) | \(0.01696 ^{\{ 4 \}}\) | \(0.01943 ^{\{ 3 \}}\) | \(0.01728 ^{\{ 14 \}}\) | \(0.01724 ^{\{ 5 \}}\) | \(0.01738 ^{\{ 8 \}}\) | |
\(\sum Ranks\) | \(17 ^{\{ 1 \}}\) | \(30 ^{\{ 2.5 \}}\) | \(62 ^{\{ 6 \}}\) | \(30 ^{\{ 2.5 \}}\) | \(42 ^{\{ 4 \}}\) | \(109 ^{\{ 13 \}}\) | \(50 ^{\{ 5 \}}\) | \(66 ^{\{ 8 \}}\) | |
150 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.04287 ^{\{ 1 \}}\) | \(0.04974 ^{\{ 2 \}}\) | \(0.05757 ^{\{ 7 \}}\) | \(0.05101 ^{\{ 3 \}}\) | \(0.06124 ^{\{ 11 \}}\) | \(0.06273 ^{\{ 13 \}}\) | \(0.0512 ^{\{ 4 \}}\) | \(0.05626 ^{\{ 6 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.10969 ^{\{ 1 \}}\) | \(0.12049 ^{\{ 5 \}}\) | \(0.13119 ^{\{ 9 \}}\) | \(0.11262 ^{\{ 2 \}}\) | \(0.11924 ^{\{ 4 \}}\) | \(0.1246 ^{\{ 7 \}}\) | \(0.12904 ^{\{ 8 \}}\) | \(0.11887 ^{\{ 3 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00281 ^{\{ 1 \}}\) | \(0.00377 ^{\{ 2 \}}\) | \(0.00535 ^{\{ 6 \}}\) | \(0.00384 ^{\{ 3 \}}\) | \(0.00622 ^{\{ 11 \}}\) | \(0.00616 ^{\{ 10 \}}\) | \(0.00404 ^{\{ 4 \}}\) | \(0.00547 ^{\{ 7.5 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.01988 ^{\{ 1 \}}\) | \(0.02282 ^{\{ 4 \}}\) | \(0.02661 ^{\{ 9 \}}\) | \(0.02042 ^{\{ 2 \}}\) | \(0.02119 ^{\{ 3 \}}\) | \(0.02394 ^{\{ 7 \}}\) | \(0.02533 ^{\{ 8 \}}\) | \(0.02321 ^{\{ 6 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.04764 ^{\{ 1 \}}\) | \(0.05527 ^{\{ 2 \}}\) | \(0.06397 ^{\{ 7 \}}\) | \(0.05668 ^{\{ 3 \}}\) | \(0.06805 ^{\{ 11 \}}\) | \(0.0697 ^{\{ 13 \}}\) | \(0.05689 ^{\{ 4 \}}\) | \(0.06251 ^{\{ 6 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.04388 ^{\{ 1 \}}\) | \(0.0482 ^{\{ 5 \}}\) | \(0.05247 ^{\{ 9 \}}\) | \(0.04505 ^{\{ 2 \}}\) | \(0.04769 ^{\{ 4 \}}\) | \(0.04984 ^{\{ 7 \}}\) | \(0.05161 ^{\{ 8 \}}\) | \(0.04755 ^{\{ 3 \}}\) | |
\(\pmb K{_4}\) | \(0.01971 ^{\{ 1 \}}\) | \(0.02116 ^{\{ 4 \}}\) | \(0.02182 ^{\{ 5 \}}\) | \(0.02007 ^{\{ 2 \}}\) | \(0.02236 ^{\{ 7 \}}\) | \(0.02407 ^{\{ 12 \}}\) | \(0.02239 ^{\{ 8 \}}\) | \(0.0208 ^{\{ 3 \}}\) | |
\(\pmb K{_5}\) | \(0.03086 ^{\{ 1 \}}\) | \(0.03373 ^{\{ 3 \}}\) | \(0.03564 ^{\{ 5 \}}\) | \(0.03265 ^{\{ 2 \}}\) | \(0.03633 ^{\{ 7 \}}\) | \(0.03849 ^{\{ 11 \}}\) | \(0.03566 ^{\{ 6 \}}\) | \(0.03395 ^{\{ 4 \}}\) | |
\(\pmb K{_6}\) | \(0.01207 ^{\{ 1 \}}\) | \(0.01156 ^{\{ 3 \}}\) | \(0.01277 ^{\{ 5 \}}\) | \(0.01229 ^{\{ 2 \}}\) | \(0.01277 ^{\{ 7 \}}\) | \(0.01184 ^{\{ 11 \}}\) | \(0.01113 ^{\{ 6 \}}\) | \(0.01199 ^{\{ 4 \}}\) | |
\(\sum Ranks\) | \(13 ^{\{ 1 \}}\) | \(29 ^{\{ 3 \}}\) | \(64 ^{\{ 6 \}}\) | \(25 ^{\{ 2 \}}\) | \(66 ^{\{ 7 \}}\) | \(83 ^{\{ 10 \}}\) | \(51 ^{\{ 5 \}}\) | \(42.5 ^{\{ 4 \}}\) |
300 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.03574 ^{\{ 3 \}}\) | \(0.03508 ^{\{ 2 \}}\) | \(0.04609 ^{\{ 12 \}}\) | \(0.03301 ^{\{ 1 \}}\) | \(0.04217 ^{\{ 10 \}}\) | \(0.05837 ^{\{ 15 \}}\) | \(0.03693 ^{\{ 4 \}}\) | \(0.04101 ^{\{ 9 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.07413 ^{\{ 1 \}}\) | \(0.08575 ^{\{ 6 \}}\) | \(0.09093 ^{\{ 7 \}}\) | \(0.09373 ^{\{ 11 \}}\) | \(0.09289 ^{\{ 8 \}}\) | \(0.0825 ^{\{ 2 \}}\) | \(0.08449 ^{\{ 4 \}}\) | \(0.0833 ^{\{ 3 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00201 ^{\{ 3 \}}\) | \(0.00193 ^{\{ 2 \}}\) | \(0.00318 ^{\{ 11 \}}\) | \(0.00177 ^{\{ 1 \}}\) | \(0.00299 ^{\{ 10 \}}\) | \(0.00501 ^{\{ 15 \}}\) | \(0.00211 ^{\{ 4 \}}\) | \(0.00233 ^{\{ 7 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00927 ^{\{ 1 \}}\) | \(0.01158 ^{\{ 6 \}}\) | \(0.01299 ^{\{ 7 \}}\) | \(0.01331 ^{\{ 8 \}}\) | \(0.0144 ^{\{ 11 \}}\) | \(0.01001 ^{\{ 2 \}}\) | \(0.01017 ^{\{ 3 \}}\) | \(0.01122 ^{\{ 5 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.03971 ^{\{ 3 \}}\) | \(0.03898 ^{\{ 2 \}}\) | \(0.05121 ^{\{ 12 \}}\) | \(0.03668 ^{\{ 1 \}}\) | \(0.04686 ^{\{ 10 \}}\) | \(0.06485 ^{\{ 15 \}}\) | \(0.04103 ^{\{ 4 \}}\) | \(0.04556 ^{\{ 9 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.02965 ^{\{ 1 \}}\) | \(0.0343 ^{\{ 6 \}}\) | \(0.03637 ^{\{ 7 \}}\) | \(0.03749 ^{\{ 11 \}}\) | \(0.03716 ^{\{ 8 \}}\) | \(0.033 ^{\{ 2 \}}\) | \(0.0338 ^{\{ 4 \}}\) | \(0.03332 ^{\{ 3 \}}\) | |
\(\pmb K{_4}\) | \(0.01395 ^{\{ 1 \}}\) | \(0.01445 ^{\{ 2 \}}\) | \(0.01533 ^{\{ 6 \}}\) | \(0.01611 ^{\{ 9 \}}\) | \(0.01604 ^{\{ 8 \}}\) | \(0.01858 ^{\{ 14 \}}\) | \(0.01489 ^{\{ 3 \}}\) | \(0.015 ^{\{ 4 \}}\) | |
\(\pmb K{_5}\) | \(0.02212 ^{\{ 1 \}}\) | \(0.02329 ^{\{ 2 \}}\) | \(0.02583 ^{\{ 8 \}}\) | \(0.02517 ^{\{ 6 \}}\) | \(0.02621 ^{\{ 9 \}}\) | \(0.03016 ^{\{ 14 \}}\) | \(0.02393 ^{\{ 3 \}}\) | \(0.02456 ^{\{ 4 \}}\) | |
\(\pmb K{_6}\) | \(0.00733 ^{\{ 1 \}}\) | \(0.00757 ^{\{ 2 \}}\) | \(0.00841 ^{\{ 8 \}}\) | \(0.00789 ^{\{ 6 \}}\) | \(0.00783 ^{\{ 9 \}}\) | \(0.00842 ^{\{ 14 \}}\) | \(0.00747 ^{\{ 3 \}}\) | \(0.00769 ^{\{ 4 \}}\) | |
\(\sum Ranks\) | \(15 ^{\{ 1 \}}\) | \(31 ^{\{ 2.5 \}}\) | \(77 ^{\{ 9 \}}\) | \(54 ^{\{ 5 \}}\) | \(79 ^{\{ 10 \}}\) | \(87 ^{\{ 11 \}}\) | \(31 ^{\{ 2.5 \}}\) | \(48 ^{\{ 4 \}}\) | |
400 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.02643 ^{\{ 1 \}}\) | \(0.03491 ^{\{ 6 \}}\) | \(0.03775 ^{\{ 11 \}}\) | \(0.02727 ^{\{ 2 \}}\) | \(0.036 ^{\{ 8 \}}\) | \(0.04426 ^{\{ 15 \}}\) | \(0.03415 ^{\{ 5 \}}\) | \(0.03747 ^{\{ 10 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.07406 ^{\{ 6 \}}\) | \(0.07465 ^{\{ 7 \}}\) | \(0.06949 ^{\{ 2 \}}\) | \(0.0791 ^{\{ 10 \}}\) | \(0.0846 ^{\{ 11 \}}\) | \(0.0768 ^{\{ 8 \}}\) | \(0.06856 ^{\{ 1 \}}\) | \(0.07306 ^{\{ 5 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00113 ^{\{ 2 \}}\) | \(0.0018 ^{\{ 6 \}}\) | \(0.00222 ^{\{ 11 \}}\) | \(0.00112 ^{\{ 1 \}}\) | \(0.00202 ^{\{ 7 \}}\) | \(0.003 ^{\{ 15 \}}\) | \(0.00175 ^{\{ 5 \}}\) | \(0.00209 ^{\{ 9 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00822 ^{\{ 3 \}}\) | \(0.00835 ^{\{ 4 \}}\) | \(0.00848 ^{\{ 5.5 \}}\) | \(0.00952 ^{\{ 10 \}}\) | \(0.01089 ^{\{ 11 \}}\) | \(0.00932 ^{\{ 8 \}}\) | \(0.00717 ^{\{ 1 \}}\) | \(0.00848 ^{\{ 5.5 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.02937 ^{\{ 1 \}}\) | \(0.03879 ^{\{ 6 \}}\) | \(0.04195 ^{\{ 11 \}}\) | \(0.0303 ^{\{ 2 \}}\) | \(0.04 ^{\{ 8 \}}\) | \(0.04918 ^{\{ 15 \}}\) | \(0.03794 ^{\{ 5 \}}\) | \(0.04164 ^{\{ 10 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.02962 ^{\{ 6 \}}\) | \(0.02986 ^{\{ 7 \}}\) | \(0.0278 ^{\{ 2 \}}\) | \(0.03164 ^{\{ 10 \}}\) | \(0.03384 ^{\{ 11 \}}\) | \(0.03072 ^{\{ 8 \}}\) | \(0.02742 ^{\{ 1 \}}\) | \(0.02923 ^{\{ 5 \}}\) | |
\(\pmb K{_4}\) | \(0.01298 ^{\{ 4 \}}\) | \(0.01362 ^{\{ 7 \}}\) | \(0.01257 ^{\{ 2 \}}\) | \(0.01374 ^{\{ 9 \}}\) | \(0.01432 ^{\{ 10 \}}\) | \(0.01604 ^{\{ 11 \}}\) | \(0.0122 ^{\{ 1 \}}\) | \(0.01312 ^{\{ 5 \}}\) | |
\(\pmb K{_5}\) | \(0.02031 ^{\{ 2 \}}\) | \(0.02173 ^{\{ 7 \}}\) | \(0.02064 ^{\{ 4 \}}\) | \(0.02144 ^{\{ 6 \}}\) | \(0.02326 ^{\{ 10 \}}\) | \(0.02553 ^{\{ 12 \}}\) | \(0.01981 ^{\{ 1 \}}\) | \(0.02121 ^{\{ 5 \}}\) | |
\(\pmb K{_6}\) | \(0.00649 ^{\{ 2 \}}\) | \(0.00633 ^{\{ 7 \}}\) | \(0.00685 ^{\{ 4 \}}\) | \(0.00641 ^{\{ 6 \}}\) | \(0.00659 ^{\{ 10 \}}\) | \(0.00666 ^{\{ 12 \}}\) | \(0.00578 ^{\{ 1 \}}\) | \(0.00629 ^{\{ 5 \}}\) | |
\(\sum Ranks\) | \(30 ^{\{ 2 \}}\) | \(53 ^{\{ 4 \}}\) | \(56.5 ^{\{ 6.5 \}}\) | \(54 ^{\{ 5 \}}\) | \(82 ^{\{ 10 \}}\) | \(99 ^{\{ 12 \}}\) | \(21 ^{\{ 1 \}}\) | \(56.5 ^{\{ 6.5 \}}\) | |
500 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.02559 ^{\{ 1 \}}\) | \(0.02916 ^{\{ 8 \}}\) | \(0.02984 ^{\{ 9 \}}\) | \(0.02662 ^{\{ 2 \}}\) | \(0.03149 ^{\{ 10 \}}\) | \(0.03901 ^{\{ 15 \}}\) | \(0.02871 ^{\{ 7 \}}\) | \(0.02763 ^{\{ 5 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.06219 ^{\{ 3 \}}\) | \(0.07173 ^{\{ 10 \}}\) | \(0.06835 ^{\{ 6 \}}\) | \(0.06153 ^{\{ 2 \}}\) | \(0.07745 ^{\{ 11 \}}\) | \(0.06963 ^{\{ 7 \}}\) | \(0.06437 ^{\{ 5 \}}\) | \(0.06402 ^{\{ 4 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00104 ^{\{ 1 \}}\) | \(0.00139 ^{\{ 8 \}}\) | \(0.00147 ^{\{ 9 \}}\) | \(0.00105 ^{\{ 2 \}}\) | \(0.00153 ^{\{ 11 \}}\) | \(0.00248 ^{\{ 15 \}}\) | \(0.00128 ^{\{ 6 \}}\) | \(0.00118 ^{\{ 4 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.0063 ^{\{ 3 \}}\) | \(0.00741 ^{\{ 6 \}}\) | \(0.00749 ^{\{ 7 \}}\) | \(0.00586 ^{\{ 1 \}}\) | \(0.00946 ^{\{ 11 \}}\) | \(0.00778 ^{\{ 8 \}}\) | \(0.00613 ^{\{ 2 \}}\) | \(0.0065 ^{\{ 4 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.02843 ^{\{ 1 \}}\) | \(0.0324 ^{\{ 8 \}}\) | \(0.03315 ^{\{ 9 \}}\) | \(0.02958 ^{\{ 2 \}}\) | \(0.03499 ^{\{ 10 \}}\) | \(0.04335 ^{\{ 15 \}}\) | \(0.0319 ^{\{ 7 \}}\) | \(0.0307 ^{\{ 5 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.02488 ^{\{ 3 \}}\) | \(0.02869 ^{\{ 10 \}}\) | \(0.02734 ^{\{ 6 \}}\) | \(0.02461 ^{\{ 2 \}}\) | \(0.03098 ^{\{ 11 \}}\) | \(0.02785 ^{\{ 7 \}}\) | \(0.02575 ^{\{ 5 \}}\) | \(0.02561 ^{\{ 4 \}}\) | |
\(\pmb K{_4}\) | \(0.01067 ^{\{ 1 \}}\) | \(0.01208 ^{\{ 7.5 \}}\) | \(0.01217 ^{\{ 9 \}}\) | \(0.01108 ^{\{ 2 \}}\) | \(0.01381 ^{\{ 12 \}}\) | \(0.01437 ^{\{ 13 \}}\) | \(0.01144 ^{\{ 5 \}}\) | \(0.01122 ^{\{ 4 \}}\) | |
\(\pmb K{_5}\) | \(0.01709 ^{\{ 1 \}}\) | \(0.01953 ^{\{ 8 \}}\) | \(0.01945 ^{\{ 7 \}}\) | \(0.01759 ^{\{ 2 \}}\) | \(0.022 ^{\{ 11 \}}\) | \(0.02315 ^{\{ 13 \}}\) | \(0.01832 ^{\{ 5 \}}\) | \(0.01793 ^{\{ 4 \}}\) | |
\(\pmb K{_6}\) | \(0.00547 ^{\{ 1 \}}\) | \(0.00557 ^{\{ 8 \}}\) | \(0.00614 ^{\{ 7 \}}\) | \(0.00563 ^{\{ 2 \}}\) | \(0.00566 ^{\{ 11 \}}\) | \(0.00579 ^{\{ 13 \}}\) | \(0.00527 ^{\{ 5 \}}\) | \(0.00556 ^{\{ 4 \}}\) | |
\(\sum Ranks\) | \(16 ^{\{ 1 \}}\) | \(69.5 ^{\{ 7 \}}\) | \(71 ^{\{ 8 \}}\) | \(20 ^{\{ 2 \}}\) | \(93 ^{\{ 11 \}}\) | \(100 ^{\{ 12 \}}\) | \(43 ^{\{ 5 \}}\) | \(37 ^{\{ 3 \}}\) |
n | Est. | LTADE | MSADE | MSALDE | ADSOE | KE | MSSD | MSSLD | MSLND |
|---|---|---|---|---|---|---|---|---|---|
30 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.13838 ^{\{ 9 \}}\) | \(0.14739 ^{\{ 11 \}}\) | \(0.11228 ^{\{ 4 \}}\) | \(0.17472 ^{\{ 14 \}}\) | \(0.17112 ^{\{ 13 \}}\) | \(0.17615 ^{\{ 15 \}}\) | \(0.1137 ^{\{ 5 \}}\) | \(0.19022 ^{\{ 16 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.35375 ^{\{ 14 \}}\) | \(0.2841 ^{\{ 8 \}}\) | \(0.24206 ^{\{ 4 \}}\) | \(0.45943 ^{\{ 16 \}}\) | \(0.34804 ^{\{ 13 \}}\) | \(0.37926 ^{\{ 15 \}}\) | \(0.26793 ^{\{ 7 \}}\) | \(0.32521 ^{\{ 12 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.03314 ^{\{ 9 \}}\) | \(0.03463 ^{\{ 10 \}}\) | \(0.01987 ^{\{ 4 \}}\) | \(0.04855 ^{\{ 15 \}}\) | \(0.04731 ^{\{ 14 \}}\) | \(0.04726 ^{\{ 13 \}}\) | \(0.02189 ^{\{ 5 \}}\) | \(0.05491 ^{\{ 16 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.22551 ^{\{ 14 \}}\) | \(0.12779 ^{\{ 8 \}}\) | \(0.09578 ^{\{ 3 \}}\) | \(0.38981 ^{\{ 16 \}}\) | \(0.20856 ^{\{ 13 \}}\) | \(0.27573 ^{\{ 15 \}}\) | \(0.11406 ^{\{ 7 \}}\) | \(0.16291 ^{\{ 12 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.15376 ^{\{ 9 \}}\) | \(0.16376 ^{\{ 11 \}}\) | \(0.12475 ^{\{ 4 \}}\) | \(0.19413 ^{\{ 14 \}}\) | \(0.19014 ^{\{ 13 \}}\) | \(0.19573 ^{\{ 15 \}}\) | \(0.12633 ^{\{ 5 \}}\) | \(0.21136 ^{\{ 16 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.1415 ^{\{ 14 \}}\) | \(0.11364 ^{\{ 8 \}}\) | \(0.09682 ^{\{ 4 \}}\) | \(0.18377 ^{\{ 16 \}}\) | \(0.13922 ^{\{ 13 \}}\) | \(0.1517 ^{\{ 15 \}}\) | \(0.10717 ^{\{ 7 \}}\) | \(0.13008 ^{\{ 12 \}}\) | |
\(\pmb K{_4}\) | \(0.05197 ^{\{ 11 \}}\) | \(0.05525 ^{\{ 12 \}}\) | \(0.04628 ^{\{ 4 \}}\) | \(0.05933 ^{\{ 14 \}}\) | \(0.05894 ^{\{ 13 \}}\) | \(0.06674 ^{\{ 16 \}}\) | \(0.04886 ^{\{ 8 \}}\) | \(0.06503 ^{\{ 15 \}}\) | |
\(\pmb K{_5}\) | \(0.08691 ^{\{ 11 \}}\) | \(0.08865 ^{\{ 12 \}}\) | \(0.0736 ^{\{ 2 \}}\) | \(0.10342 ^{\{ 14 \}}\) | \(0.09607 ^{\{ 13 \}}\) | \(0.10722 ^{\{ 16 \}}\) | \(0.07582 ^{\{ 7 \}}\) | \(0.10582 ^{\{ 15 \}}\) | |
\(\pmb K{_6}\) | \(0.04088 ^{\{ 11 \}}\) | \(0.04316 ^{\{ 12 \}}\) | \(0.04286 ^{\{ 2 \}}\) | \(0.06951 ^{\{ 14 \}}\) | \(0.03696 ^{\{ 13 \}}\) | \(0.0497 ^{\{ 16 \}}\) | \(0.03835 ^{\{ 7 \}}\) | \(0.05231 ^{\{ 15 \}}\) | |
\(\sum Ranks\) | \(102 ^{\{ 12 \}}\) | \(93 ^{\{ 11 \}}\) | \(41 ^{\{ 3 \}}\) | \(135 ^{\{ 16 \}}\) | \(114 ^{\{ 13 \}}\) | \(134 ^{\{ 15 \}}\) | \(61 ^{\{ 9 \}}\) | \(129 ^{\{ 14 \}}\) | |
80 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.08276 ^{\{ 10 \}}\) | \(0.09199 ^{\{ 12 \}}\) | \(0.07356 ^{\{ 6 \}}\) | \(0.10452 ^{\{ 16 \}}\) | \(0.08717 ^{\{ 11 \}}\) | \(0.09444 ^{\{ 14 \}}\) | \(0.07235 ^{\{ 5 \}}\) | \(0.09287 ^{\{ 13 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.18852 ^{\{ 10 \}}\) | \(0.23288 ^{\{ 15 \}}\) | \(0.19233 ^{\{ 14 \}}\) | \(0.23462 ^{\{ 16 \}}\) | \(0.18139 ^{\{ 8 \}}\) | \(0.1918 ^{\{ 13 \}}\) | \(0.17839 ^{\{ 7 \}}\) | \(0.18284 ^{\{ 9 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.01045 ^{\{ 9 \}}\) | \(0.01308 ^{\{ 13 \}}\) | \(0.0085 ^{\{ 6 \}}\) | \(0.01623 ^{\{ 16 \}}\) | \(0.01271 ^{\{ 11 \}}\) | \(0.01284 ^{\{ 12 \}}\) | \(0.00819 ^{\{ 4 \}}\) | \(0.01348 ^{\{ 14 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.05618 ^{\{ 12 \}}\) | \(0.09466 ^{\{ 15 \}}\) | \(0.05381 ^{\{ 10 \}}\) | \(0.09795 ^{\{ 16 \}}\) | \(0.04806 ^{\{ 7 \}}\) | \(0.05749 ^{\{ 13 \}}\) | \(0.0491 ^{\{ 8 \}}\) | \(0.05774 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.09196 ^{\{ 10 \}}\) | \(0.10221 ^{\{ 12 \}}\) | \(0.08174 ^{\{ 6 \}}\) | \(0.11613 ^{\{ 16 \}}\) | \(0.09685 ^{\{ 11 \}}\) | \(0.10493 ^{\{ 14 \}}\) | \(0.08039 ^{\{ 5 \}}\) | \(0.10319 ^{\{ 13 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.07541 ^{\{ 10 \}}\) | \(0.09315 ^{\{ 15 \}}\) | \(0.07693 ^{\{ 14 \}}\) | \(0.09385 ^{\{ 16 \}}\) | \(0.07256 ^{\{ 8 \}}\) | \(0.07672 ^{\{ 13 \}}\) | \(0.07136 ^{\{ 7 \}}\) | \(0.07314 ^{\{ 9 \}}\) | |
\(\pmb K{_4}\) | \(0.03141 ^{\{ 8 \}}\) | \(0.03767 ^{\{ 15 \}}\) | \(0.03511 ^{\{ 14 \}}\) | \(0.03501 ^{\{ 13 \}}\) | \(0.02956 ^{\{ 4 \}}\) | \(0.03497 ^{\{ 12 \}}\) | \(0.03259 ^{\{ 10 \}}\) | \(0.03345 ^{\{ 11 \}}\) | |
\(\pmb K{_5}\) | \(0.05161 ^{\{ 10 \}}\) | \(0.06105 ^{\{ 15 \}}\) | \(0.05436 ^{\{ 12 \}}\) | \(0.06149 ^{\{ 16 \}}\) | \(0.05014 ^{\{ 7 \}}\) | \(0.05593 ^{\{ 13 \}}\) | \(0.05153 ^{\{ 9 \}}\) | \(0.05397 ^{\{ 11 \}}\) | |
\(\pmb K{_6}\) | \(0.02211 ^{\{ 10 \}}\) | \(0.02397 ^{\{ 15 \}}\) | \(0.02326 ^{\{ 12 \}}\) | \(0.03656 ^{\{ 16 \}}\) | \(0.02125 ^{\{ 7 \}}\) | \(0.02679 ^{\{ 13 \}}\) | \(0.02124 ^{\{ 9 \}}\) | \(0.02603 ^{\{ 11 \}}\) | |
\(\sum Ranks\) | \(90 ^{\{ 10 \}}\) | \(125 ^{\{ 15 \}}\) | \(94 ^{\{ 11 \}}\) | \(141 ^{\{ 16 \}}\) | \(77 ^{\{ 9 \}}\) | \(119 ^{\{ 14 \}}\) | \(64 ^{\{ 7 \}}\) | \(108 ^{\{ 12 \}}\) | |
150 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.06075 ^{\{ 9 \}}\) | \(0.06021 ^{\{ 8 \}}\) | \(0.06209 ^{\{ 12 \}}\) | \(0.08076 ^{\{ 16 \}}\) | \(0.06097 ^{\{ 10 \}}\) | \(0.06632 ^{\{ 14 \}}\) | \(0.05142 ^{\{ 5 \}}\) | \(0.07299 ^{\{ 15 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.14801 ^{\{ 13 \}}\) | \(0.14639 ^{\{ 12 \}}\) | \(0.12321 ^{\{ 6 \}}\) | \(0.21642 ^{\{ 16 \}}\) | \(0.13288 ^{\{ 10 \}}\) | \(0.15496 ^{\{ 15 \}}\) | \(0.14212 ^{\{ 11 \}}\) | \(0.15102 ^{\{ 14 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00625 ^{\{ 12 \}}\) | \(0.00578 ^{\{ 9 \}}\) | \(0.00547 ^{\{ 7.5 \}}\) | \(0.01091 ^{\{ 16 \}}\) | \(0.00632 ^{\{ 13 \}}\) | \(0.00669 ^{\{ 14 \}}\) | \(0.00407 ^{\{ 5 \}}\) | \(0.00787 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.03552 ^{\{ 13 \}}\) | \(0.03284 ^{\{ 12 \}}\) | \(0.0229 ^{\{ 5 \}}\) | \(0.0792 ^{\{ 16 \}}\) | \(0.03061 ^{\{ 10 \}}\) | \(0.03669 ^{\{ 15 \}}\) | \(0.03175 ^{\{ 11 \}}\) | \(0.03643 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.0675 ^{\{ 9 \}}\) | \(0.0669 ^{\{ 8 \}}\) | \(0.06899 ^{\{ 12 \}}\) | \(0.08974 ^{\{ 16 \}}\) | \(0.06774 ^{\{ 10 \}}\) | \(0.07369 ^{\{ 14 \}}\) | \(0.05713 ^{\{ 5 \}}\) | \(0.0811 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.0592 ^{\{ 13 \}}\) | \(0.05856 ^{\{ 12 \}}\) | \(0.04928 ^{\{ 6 \}}\) | \(0.08657 ^{\{ 16 \}}\) | \(0.05315 ^{\{ 10 \}}\) | \(0.06198 ^{\{ 15 \}}\) | \(0.05685 ^{\{ 11 \}}\) | \(0.06041 ^{\{ 14 \}}\) | |
\(\pmb K{_4}\) | \(0.02324 ^{\{ 9 \}}\) | \(0.02638 ^{\{ 13 \}}\) | \(0.02325 ^{\{ 10 \}}\) | \(0.03056 ^{\{ 16 \}}\) | \(0.02228 ^{\{ 6 \}}\) | \(0.02855 ^{\{ 15 \}}\) | \(0.024 ^{\{ 11 \}}\) | \(0.02708 ^{\{ 14 \}}\) | |
\(\pmb K{_5}\) | \(0.03857 ^{\{ 12 \}}\) | \(0.04141 ^{\{ 13 \}}\) | \(0.03722 ^{\{ 9 \}}\) | \(0.05269 ^{\{ 16 \}}\) | \(0.03672 ^{\{ 8 \}}\) | \(0.04504 ^{\{ 15 \}}\) | \(0.03759 ^{\{ 10 \}}\) | \(0.04449 ^{\{ 14 \}}\) | |
\(\pmb K{_6}\) | \(0.01454 ^{\{ 12 \}}\) | \(0.01633 ^{\{ 13 \}}\) | \(0.01518 ^{\{ 9 \}}\) | \(0.02992 ^{\{ 16 \}}\) | \(0.01341 ^{\{ 8 \}}\) | \(0.01783 ^{\{ 15 \}}\) | \(0.01395 ^{\{ 10 \}}\) | \(0.01911 ^{\{ 14 \}}\) | |
\(\sum Ranks\) | \(101 ^{\{ 13 \}}\) | \(100 ^{\{ 12 \}}\) | \(79.5 ^{\{ 9 \}}\) | \(144 ^{\{ 16 \}}\) | \(86 ^{\{ 11 \}}\) | \(131 ^{\{ 15 \}}\) | \(79 ^{\{ 8 \}}\) | \(130 ^{\{ 14 \}}\) |
300 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.03982 ^{\{ 7 \}}\) | \(0.03775 ^{\{ 5 \}}\) | \(0.04031 ^{\{ 8 \}}\) | \(0.06145 ^{\{ 16 \}}\) | \(0.04526 ^{\{ 11 \}}\) | \(0.0471 ^{\{ 13 \}}\) | \(0.03859 ^{\{ 6 \}}\) | \(0.04722 ^{\{ 14 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.0936 ^{\{ 10 \}}\) | \(0.11312 ^{\{ 15 \}}\) | \(0.09393 ^{\{ 12 \}}\) | \(0.14583 ^{\{ 16 \}}\) | \(0.08511 ^{\{ 5 \}}\) | \(0.10421 ^{\{ 13 \}}\) | \(0.09321 ^{\{ 9 \}}\) | \(0.11086 ^{\{ 14 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00256 ^{\{ 8 \}}\) | \(0.00222 ^{\{ 6 \}}\) | \(0.00259 ^{\{ 9 \}}\) | \(0.00593 ^{\{ 16 \}}\) | \(0.00345 ^{\{ 14 \}}\) | \(0.0033 ^{\{ 12 \}}\) | \(0.00215 ^{\{ 5 \}}\) | \(0.00336 ^{\{ 13 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.01355 ^{\{ 10 \}}\) | \(0.01831 ^{\{ 14 \}}\) | \(0.01336 ^{\{ 9 \}}\) | \(0.03378 ^{\{ 16 \}}\) | \(0.0111 ^{\{ 4 \}}\) | \(0.01683 ^{\{ 13 \}}\) | \(0.01476 ^{\{ 12 \}}\) | \(0.01904 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.04424 ^{\{ 7 \}}\) | \(0.04195 ^{\{ 5 \}}\) | \(0.04479 ^{\{ 8 \}}\) | \(0.06828 ^{\{ 16 \}}\) | \(0.05029 ^{\{ 11 \}}\) | \(0.05234 ^{\{ 13 \}}\) | \(0.04288 ^{\{ 6 \}}\) | \(0.05246 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.03744 ^{\{ 10 \}}\) | \(0.04525 ^{\{ 15 \}}\) | \(0.03757 ^{\{ 12 \}}\) | \(0.05833 ^{\{ 16 \}}\) | \(0.03405 ^{\{ 5 \}}\) | \(0.04168 ^{\{ 13 \}}\) | \(0.03728 ^{\{ 9 \}}\) | \(0.04434 ^{\{ 14 \}}\) | |
\(\pmb K{_4}\) | \(0.01569 ^{\{ 7 \}}\) | \(0.01844 ^{\{ 12 \}}\) | \(0.01736 ^{\{ 11 \}}\) | \(0.02116 ^{\{ 16 \}}\) | \(0.01518 ^{\{ 5 \}}\) | \(0.01849 ^{\{ 13 \}}\) | \(0.01686 ^{\{ 10 \}}\) | \(0.01912 ^{\{ 15 \}}\) | |
\(\pmb K{_5}\) | \(0.02554 ^{\{ 7 \}}\) | \(0.02914 ^{\{ 12 \}}\) | \(0.02726 ^{\{ 11 \}}\) | \(0.03719 ^{\{ 16 \}}\) | \(0.02492 ^{\{ 5 \}}\) | \(0.03005 ^{\{ 13 \}}\) | \(0.02644 ^{\{ 10 \}}\) | \(0.0313 ^{\{ 15 \}}\) | |
\(\pmb K{_6}\) | \(0.00926 ^{\{ 7 \}}\) | \(0.01053 ^{\{ 12 \}}\) | \(0.00984 ^{\{ 11 \}}\) | \(0.01807 ^{\{ 16 \}}\) | \(0.00946 ^{\{ 5 \}}\) | \(0.01168 ^{\{ 13 \}}\) | \(0.00917 ^{\{ 10 \}}\) | \(0.01227 ^{\{ 15 \}}\) | |
\(\sum Ranks\) | \(76 ^{\{ 7.5 \}}\) | \(97 ^{\{ 13 \}}\) | \(92 ^{\{ 12 \}}\) | \(144 ^{\{ 16 \}}\) | \(71 ^{\{ 6 \}}\) | \(117 ^{\{ 14 \}}\) | \(76 ^{\{ 7.5 \}}\) | \(129 ^{\{ 15 \}}\) | |
400 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.03532 ^{\{ 7 \}}\) | \(0.03668 ^{\{ 9 \}}\) | \(0.03178 ^{\{ 4 \}}\) | \(0.05381 ^{\{ 16 \}}\) | \(0.04068 ^{\{ 14 \}}\) | \(0.04064 ^{\{ 13 \}}\) | \(0.02885 ^{\{ 3 \}}\) | \(0.03898 ^{\{ 12 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.07865 ^{\{ 9 \}}\) | \(0.09417 ^{\{ 15 \}}\) | \(0.0911 ^{\{ 13 \}}\) | \(0.12089 ^{\{ 16 \}}\) | \(0.07088 ^{\{ 3 \}}\) | \(0.09022 ^{\{ 12 \}}\) | \(0.07111 ^{\{ 4 \}}\) | \(0.0941 ^{\{ 14 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.0021 ^{\{ 10 \}}\) | \(0.00207 ^{\{ 8 \}}\) | \(0.00148 ^{\{ 4 \}}\) | \(0.00448 ^{\{ 16 \}}\) | \(0.00237 ^{\{ 13 \}}\) | \(0.00245 ^{\{ 14 \}}\) | \(0.00141 ^{\{ 3 \}}\) | \(0.00228 ^{\{ 12 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00933 ^{\{ 9 \}}\) | \(0.01314 ^{\{ 13 \}}\) | \(0.01221 ^{\{ 12 \}}\) | \(0.02238 ^{\{ 16 \}}\) | \(0.00807 ^{\{ 2 \}}\) | \(0.01327 ^{\{ 14 \}}\) | \(0.00888 ^{\{ 7 \}}\) | \(0.01628 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.03925 ^{\{ 7 \}}\) | \(0.04076 ^{\{ 9 \}}\) | \(0.03532 ^{\{ 4 \}}\) | \(0.05979 ^{\{ 16 \}}\) | \(0.04521 ^{\{ 14 \}}\) | \(0.04516 ^{\{ 13 \}}\) | \(0.03206 ^{\{ 3 \}}\) | \(0.04331 ^{\{ 12 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.03146 ^{\{ 9 \}}\) | \(0.03767 ^{\{ 15 \}}\) | \(0.03644 ^{\{ 13 \}}\) | \(0.04836 ^{\{ 16 \}}\) | \(0.02835 ^{\{ 3 \}}\) | \(0.03609 ^{\{ 12 \}}\) | \(0.02844 ^{\{ 4 \}}\) | \(0.03764 ^{\{ 14 \}}\) | |
\(\pmb K{_4}\) | \(0.01372 ^{\{ 8 \}}\) | \(0.01621 ^{\{ 13 \}}\) | \(0.01618 ^{\{ 12 \}}\) | \(0.01743 ^{\{ 16 \}}\) | \(0.01324 ^{\{ 6 \}}\) | \(0.01624 ^{\{ 14 \}}\) | \(0.01289 ^{\{ 3 \}}\) | \(0.01673 ^{\{ 15 \}}\) | |
\(\pmb K{_5}\) | \(0.02232 ^{\{ 9 \}}\) | \(0.0259 ^{\{ 13 \}}\) | \(0.0248 ^{\{ 11 \}}\) | \(0.03083 ^{\{ 16 \}}\) | \(0.02194 ^{\{ 8 \}}\) | \(0.02608 ^{\{ 14 \}}\) | \(0.02038 ^{\{ 3 \}}\) | \(0.0268 ^{\{ 15 \}}\) | |
\(\pmb K{_6}\) | \(0.00787 ^{\{ 9 \}}\) | \(0.00876 ^{\{ 13 \}}\) | \(0.00826 ^{\{ 11 \}}\) | \(0.01329 ^{\{ 16 \}}\) | \(0.00746 ^{\{ 8 \}}\) | \(0.00992 ^{\{ 14 \}}\) | \(0.00769 ^{\{ 3 \}}\) | \(0.01071 ^{\{ 15 \}}\) | |
\(\sum Ranks\) | \(79 ^{\{ 9 \}}\) | \(108 ^{\{ 13 \}}\) | \(85 ^{\{ 11 \}}\) | \(144 ^{\{ 16 \}}\) | \(72 ^{\{ 8 \}}\) | \(120 ^{\{ 14 \}}\) | \(40 ^{\{ 3 \}}\) | \(124 ^{\{ 15 \}}\) | |
500 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.03408 ^{\{ 12 \}}\) | \(0.03308 ^{\{ 11 \}}\) | \(0.0275 ^{\{ 4 \}}\) | \(0.04742 ^{\{ 16 \}}\) | \(0.02787 ^{\{ 6 \}}\) | \(0.03451 ^{\{ 13 \}}\) | \(0.027 ^{\{ 3 \}}\) | \(0.03807 ^{\{ 14 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.07121 ^{\{ 9 \}}\) | \(0.07824 ^{\{ 13 \}}\) | \(0.07814 ^{\{ 12 \}}\) | \(0.10285 ^{\{ 16 \}}\) | \(0.05913 ^{\{ 1 \}}\) | \(0.08422 ^{\{ 15 \}}\) | \(0.07097 ^{\{ 8 \}}\) | \(0.07995 ^{\{ 14 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00177 ^{\{ 12 \}}\) | \(0.0015 ^{\{ 10 \}}\) | \(0.00115 ^{\{ 3 \}}\) | \(0.00343 ^{\{ 16 \}}\) | \(0.0013 ^{\{ 7 \}}\) | \(0.00185 ^{\{ 13 \}}\) | \(0.00124 ^{\{ 5 \}}\) | \(0.00212 ^{\{ 14 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00781 ^{\{ 9 \}}\) | \(0.01001 ^{\{ 12 \}}\) | \(0.01004 ^{\{ 13 \}}\) | \(0.01607 ^{\{ 16 \}}\) | \(0.00664 ^{\{ 5 \}}\) | \(0.01096 ^{\{ 15 \}}\) | \(0.00816 ^{\{ 10 \}}\) | \(0.01057 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.03787 ^{\{ 12 \}}\) | \(0.03676 ^{\{ 11 \}}\) | \(0.03055 ^{\{ 4 \}}\) | \(0.05269 ^{\{ 16 \}}\) | \(0.03097 ^{\{ 6 \}}\) | \(0.03834 ^{\{ 13 \}}\) | \(0.03 ^{\{ 3 \}}\) | \(0.0423 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.02848 ^{\{ 9 \}}\) | \(0.0313 ^{\{ 13 \}}\) | \(0.03126 ^{\{ 12 \}}\) | \(0.04114 ^{\{ 16 \}}\) | \(0.02365 ^{\{ 1 \}}\) | \(0.03369 ^{\{ 15 \}}\) | \(0.02839 ^{\{ 8 \}}\) | \(0.03198 ^{\{ 14 \}}\) | |
\(\pmb K{_4}\) | \(0.01208 ^{\{ 7.5 \}}\) | \(0.01364 ^{\{ 11 \}}\) | \(0.013 ^{\{ 10 \}}\) | \(0.01491 ^{\{ 15 \}}\) | \(0.01121 ^{\{ 3 \}}\) | \(0.01475 ^{\{ 14 \}}\) | \(0.01201 ^{\{ 6 \}}\) | \(0.01523 ^{\{ 16 \}}\) | |
\(\pmb K{_5}\) | \(0.01988 ^{\{ 9 \}}\) | \(0.02205 ^{\{ 12 \}}\) | \(0.02095 ^{\{ 10 \}}\) | \(0.02628 ^{\{ 16 \}}\) | \(0.01791 ^{\{ 3 \}}\) | \(0.02338 ^{\{ 14 \}}\) | \(0.01935 ^{\{ 6 \}}\) | \(0.0243 ^{\{ 15 \}}\) | |
\(\pmb K{_6}\) | \(0.00695 ^{\{ 9 \}}\) | \(0.00766 ^{\{ 12 \}}\) | \(0.00704 ^{\{ 10 \}}\) | \(0.01103 ^{\{ 16 \}}\) | \(0.00612 ^{\{ 3 \}}\) | \(0.00819 ^{\{ 14 \}}\) | \(0.00643 ^{\{ 6 \}}\) | \(0.00825 ^{\{ 15 \}}\) | |
\(\sum Ranks\) | \(90.5 ^{\{ 10 \}}\) | \(106 ^{\{ 13 \}}\) | \(80 ^{\{ 9 \}}\) | \(143 ^{\{ 16 \}}\) | \(40 ^{\{ 4 \}}\) | \(126 ^{\{ 14 \}}\) | \(59 ^{\{ 6 \}}\) | \(130 ^{\{ 15 \}}\) |
