Table 8 Numerical values of simulation measures for \(\alpha =1.25,~\beta =0.3\) under RSS.
n | Est. | MLE | ADE | CVME | MPSE | OLSE | PCE | RTADE | WLSE |
|---|---|---|---|---|---|---|---|---|---|
30 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.0979 ^{\{ 2 \}}\) | \(0.10582 ^{\{ 3 \}}\) | \(0.12675 ^{\{ 11 \}}\) | \(0.11862 ^{\{ 6 \}}\) | \(0.11747 ^{\{ 5 \}}\) | \(0.08667 ^{\{ 1 \}}\) | \(0.12098 ^{\{ 8 \}}\) | \(0.11658 ^{\{ 4 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.05089 ^{\{ 1 \}}\) | \(0.05593 ^{\{ 3 \}}\) | \(0.06121 ^{\{ 4 \}}\) | \(0.06716 ^{\{ 10 \}}\) | \(0.06186 ^{\{ 6 \}}\) | \(0.05163 ^{\{ 2 \}}\) | \(0.06255 ^{\{ 8 \}}\) | \(0.0617 ^{\{ 5 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.01564 ^{\{ 2 \}}\) | \(0.01756 ^{\{ 3 \}}\) | \(0.02658 ^{\{ 11 \}}\) | \(0.02046 ^{\{ 4 \}}\) | \(0.02203 ^{\{ 7 \}}\) | \(0.01458 ^{\{ 1 \}}\) | \(0.02502 ^{\{ 9 \}}\) | \(0.02104 ^{\{ 5 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00399 ^{\{ 1 \}}\) | \(0.00503 ^{\{ 2 \}}\) | \(0.00567 ^{\{ 4 \}}\) | \(0.00719 ^{\{ 10 \}}\) | \(0.00625 ^{\{ 9 \}}\) | \(0.00544 ^{\{ 3 \}}\) | \(0.00618 ^{\{ 8 \}}\) | \(0.00593 ^{\{ 5 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.07832 ^{\{ 2 \}}\) | \(0.08466 ^{\{ 3 \}}\) | \(0.1014 ^{\{ 11 \}}\) | \(0.09489 ^{\{ 6 \}}\) | \(0.09398 ^{\{ 5 \}}\) | \(0.06934 ^{\{ 1 \}}\) | \(0.09678 ^{\{ 8 \}}\) | \(0.09327 ^{\{ 4 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.16962 ^{\{ 1 \}}\) | \(0.18644 ^{\{ 3 \}}\) | \(0.20404 ^{\{ 4 \}}\) | \(0.22388 ^{\{ 10 \}}\) | \(0.20621 ^{\{ 6 \}}\) | \(0.1721 ^{\{ 2 \}}\) | \(0.20851 ^{\{ 8 \}}\) | \(0.20566 ^{\{ 5 \}}\) | |
\(\pmb K{_4}\) | \(0.02973 ^{\{ 3 \}}\) | \(0.02964 ^{\{ 2 \}}\) | \(0.03213 ^{\{ 7 \}}\) | \(0.03133 ^{\{ 4 \}}\) | \(0.03231 ^{\{ 8 \}}\) | \(0.02928 ^{\{ 1 \}}\) | \(0.03211 ^{\{ 6 \}}\) | \(0.03137 ^{\{ 5 \}}\) | |
\(\pmb K{_5}\) | \(0.04934 ^{\{ 2 \}}\) | \(0.05053 ^{\{ 3 \}}\) | \(0.0549 ^{\{ 7 \}}\) | \(0.05394 ^{\{ 5 \}}\) | \(0.05521 ^{\{ 8 \}}\) | \(0.04878 ^{\{ 1 \}}\) | \(0.05467 ^{\{ 6 \}}\) | \(0.05342 ^{\{ 4 \}}\) | |
\(\pmb K{_6}\) | \(1.0362 ^{\{ 2 \}}\) | \(0.74786 ^{\{ 3 \}}\) | \(1.32434 ^{\{ 7 \}}\) | \(0.40554 ^{\{ 5 \}}\) | \(0.7737 ^{\{ 8 \}}\) | \(0.03281 ^{\{ 1 \}}\) | \(1.45491 ^{\{ 6 \}}\) | \(0.86427 ^{\{ 4 \}}\) | |
\(\sum Ranks\) | \(24 ^{\{ 2 \}}\) | \(27 ^{\{ 3 \}}\) | \(70 ^{\{ 7 \}}\) | \(57 ^{\{ 5 \}}\) | \(60 ^{\{ 6 \}}\) | \(13 ^{\{ 1 \}}\) | \(74 ^{\{ 8 \}}\) | \(44 ^{\{ 4 \}}\) | |
80 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.05936 ^{\{ 2 \}}\) | \(0.06189 ^{\{ 3 \}}\) | \(0.07323 ^{\{ 8 \}}\) | \(0.0682 ^{\{ 6 \}}\) | \(0.07019 ^{\{ 7 \}}\) | \(0.05719 ^{\{ 1 \}}\) | \(0.06808 ^{\{ 5 \}}\) | \(0.06711 ^{\{ 4 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.03187 ^{\{ 1 \}}\) | \(0.03246 ^{\{ 3 \}}\) | \(0.03666 ^{\{ 5 \}}\) | \(0.03725 ^{\{ 8 \}}\) | \(0.0368 ^{\{ 6 \}}\) | \(0.032 ^{\{ 2 \}}\) | \(0.03713 ^{\{ 7 \}}\) | \(0.0352 ^{\{ 4 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00557 ^{\{ 1 \}}\) | \(0.00624 ^{\{ 2 \}}\) | \(0.00869 ^{\{ 9 \}}\) | \(0.00693 ^{\{ 4 \}}\) | \(0.00766 ^{\{ 7 \}}\) | \(0.00652 ^{\{ 3 \}}\) | \(0.00733 ^{\{ 6 \}}\) | \(0.00696 ^{\{ 5 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00157 ^{\{ 1 \}}\) | \(0.0017 ^{\{ 2 \}}\) | \(0.00213 ^{\{ 6 \}}\) | \(0.00216 ^{\{ 7 \}}\) | \(0.00212 ^{\{ 5 \}}\) | \(0.0022 ^{\{ 8.5 \}}\) | \(0.00211 ^{\{ 4 \}}\) | \(0.0019 ^{\{ 3 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.04749 ^{\{ 2 \}}\) | \(0.04952 ^{\{ 3 \}}\) | \(0.05858 ^{\{ 8 \}}\) | \(0.05456 ^{\{ 6 \}}\) | \(0.05615 ^{\{ 7 \}}\) | \(0.04576 ^{\{ 1 \}}\) | \(0.05446 ^{\{ 5 \}}\) | \(0.05369 ^{\{ 4 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.10624 ^{\{ 1 \}}\) | \(0.1082 ^{\{ 3 \}}\) | \(0.12219 ^{\{ 5 \}}\) | \(0.12416 ^{\{ 8 \}}\) | \(0.12265 ^{\{ 6 \}}\) | \(0.10665 ^{\{ 2 \}}\) | \(0.12377 ^{\{ 7 \}}\) | \(0.11733 ^{\{ 4 \}}\) | |
\(\pmb K{_4}\) | \(0.01798 ^{\{ 2 \}}\) | \(0.01801 ^{\{ 3 \}}\) | \(0.01987 ^{\{ 8 \}}\) | \(0.01896 ^{\{ 4 \}}\) | \(0.0196 ^{\{ 7 \}}\) | \(0.01768 ^{\{ 1 \}}\) | \(0.01921 ^{\{ 5 \}}\) | \(0.01935 ^{\{ 6 \}}\) | |
\(\pmb K{_5}\) | \(0.03002 ^{\{ 2 \}}\) | \(0.03049 ^{\{ 3 \}}\) | \(0.03407 ^{\{ 8 \}}\) | \(0.03253 ^{\{ 5 \}}\) | \(0.03334 ^{\{ 7 \}}\) | \(0.02982 ^{\{ 1 \}}\) | \(0.03242 ^{\{ 4 \}}\) | \(0.03279 ^{\{ 6 \}}\) | |
\(\pmb K{_6}\) | \(0.41502 ^{\{ 2 \}}\) | \(0.34711 ^{\{ 3 \}}\) | \(0.44372 ^{\{ 8 \}}\) | \(0.20481 ^{\{ 5 \}}\) | \(0.32963 ^{\{ 7 \}}\) | \(0.01834 ^{\{ 1 \}}\) | \(0.42709 ^{\{ 4 \}}\) | \(0.37835 ^{\{ 6 \}}\) | |
\(\sum Ranks\) | \(23 ^{\{ 2 \}}\) | \(29 ^{\{ 3 \}}\) | \(71 ^{\{ 8 \}}\) | \(50 ^{\{ 5 \}}\) | \(58 ^{\{ 7 \}}\) | \(20.5 ^{\{ 1 \}}\) | \(55 ^{\{ 6 \}}\) | \(44 ^{\{ 4 \}}\) | |
150 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.04218 ^{\{ 2 \}}\) | \(0.04608 ^{\{ 3 \}}\) | \(0.05085 ^{\{ 6 \}}\) | \(0.04955 ^{\{ 5 \}}\) | \(0.05098 ^{\{ 7 \}}\) | \(0.03956 ^{\{ 1 \}}\) | \(0.05215 ^{\{ 8 \}}\) | \(0.04628 ^{\{ 4 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.0227 ^{\{ 2 \}}\) | \(0.02413 ^{\{ 3 \}}\) | \(0.02614 ^{\{ 5 \}}\) | \(0.02625 ^{\{ 7 \}}\) | \(0.02617 ^{\{ 6 \}}\) | \(0.022 ^{\{ 1 \}}\) | \(0.0276 ^{\{ 9 \}}\) | \(0.02458 ^{\{ 4 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00279 ^{\{ 1 \}}\) | \(0.00334 ^{\{ 3 \}}\) | \(0.00406 ^{\{ 6 \}}\) | \(0.0037 ^{\{ 5 \}}\) | \(0.00414 ^{\{ 7 \}}\) | \(0.00311 ^{\{ 2 \}}\) | \(0.0043 ^{\{ 8 \}}\) | \(0.00339 ^{\{ 4 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(8e-04 ^{\{ 1 \}}\) | \(0.00093 ^{\{ 2 \}}\) | \(0.00106 ^{\{ 5 \}}\) | \(0.00109 ^{\{ 6.5 \}}\) | \(0.00109 ^{\{ 6.5 \}}\) | \(0.00097 ^{\{ 4 \}}\) | \(0.00121 ^{\{ 9 \}}\) | \(0.00094 ^{\{ 3 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.03374 ^{\{ 2 \}}\) | \(0.03686 ^{\{ 3 \}}\) | \(0.04068 ^{\{ 6 \}}\) | \(0.03964 ^{\{ 5 \}}\) | \(0.04078 ^{\{ 7 \}}\) | \(0.03165 ^{\{ 1 \}}\) | \(0.04172 ^{\{ 8 \}}\) | \(0.03703 ^{\{ 4 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.07566 ^{\{ 2 \}}\) | \(0.08043 ^{\{ 3 \}}\) | \(0.08713 ^{\{ 5 \}}\) | \(0.08749 ^{\{ 7 \}}\) | \(0.08723 ^{\{ 6 \}}\) | \(0.07332 ^{\{ 1 \}}\) | \(0.092 ^{\{ 9 \}}\) | \(0.08193 ^{\{ 4 \}}\) | |
\(\pmb K{_4}\) | \(0.01335 ^{\{ 3 \}}\) | \(0.01346 ^{\{ 4 \}}\) | \(0.0143 ^{\{ 8 \}}\) | \(0.01331 ^{\{ 2 \}}\) | \(0.01416 ^{\{ 6 \}}\) | \(0.01318 ^{\{ 1 \}}\) | \(0.01419 ^{\{ 7 \}}\) | \(0.01354 ^{\{ 5 \}}\) | |
\(\pmb K{_5}\) | \(0.02227 ^{\{ 2 \}}\) | \(0.02282 ^{\{ 3.5 \}}\) | \(0.02426 ^{\{ 7.5 \}}\) | \(0.02282 ^{\{ 3.5 \}}\) | \(0.02421 ^{\{ 6 \}}\) | \(0.02198 ^{\{ 1 \}}\) | \(0.02426 ^{\{ 7.5 \}}\) | \(0.02289 ^{\{ 5 \}}\) | |
\(\pmb K{_6}\) | \(0.24077 ^{\{ 2 \}}\) | \(0.24239 ^{\{ 3.5 \}}\) | \(0.26909 ^{\{ 7.5 \}}\) | \(0.13368 ^{\{ 3.5 \}}\) | \(0.2293 ^{\{ 6 \}}\) | \(0.01275 ^{\{ 1 \}}\) | \(0.26762 ^{\{ 7.5 \}}\) | \(0.21217 ^{\{ 5 \}}\) | |
\(\sum Ranks\) | \(39 ^{\{ 4 \}}\) | \(33.5 ^{\{ 2 \}}\) | \(60.5 ^{\{ 7 \}}\) | \(42 ^{\{ 5 \}}\) | \(57.5 ^{\{ 6 \}}\) | \(12 ^{\{ 1 \}}\) | \(76.5 ^{\{ 8 \}}\) | \(38 ^{\{ 3 \}}\) |
300 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.02885 ^{\{ 2 \}}\) | \(0.03333 ^{\{ 5 \}}\) | \(0.03603 ^{\{ 6 \}}\) | \(0.03301 ^{\{ 3 \}}\) | \(0.03743 ^{\{ 9 \}}\) | \(0.02802 ^{\{ 1 \}}\) | \(0.0369 ^{\{ 8 \}}\) | \(0.03332 ^{\{ 4 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.01622 ^{\{ 2 \}}\) | \(0.01764 ^{\{ 4 \}}\) | \(0.01829 ^{\{ 7 \}}\) | \(0.01787 ^{\{ 5 \}}\) | \(0.0192 ^{\{ 8 \}}\) | \(0.01513 ^{\{ 1 \}}\) | \(0.01972 ^{\{ 9 \}}\) | \(0.01753 ^{\{ 3 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.0013 ^{\{ 1 \}}\) | \(0.00172 ^{\{ 5 \}}\) | \(0.00205 ^{\{ 6 \}}\) | \(0.00167 ^{\{ 3 \}}\) | \(0.00214 ^{\{ 7 \}}\) | \(0.00158 ^{\{ 2 \}}\) | \(0.00221 ^{\{ 9 \}}\) | \(0.00169 ^{\{ 4 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00041 ^{\{ 1 \}}\) | \(0.00047 ^{\{ 2.5 \}}\) | \(0.00053 ^{\{ 6.5 \}}\) | \(5e-04 ^{\{ 4.5 \}}\) | \(0.00057 ^{\{ 8 \}}\) | \(5e-04 ^{\{ 4.5 \}}\) | \(0.00063 ^{\{ 9 \}}\) | \(0.00047 ^{\{ 2.5 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.02308 ^{\{ 2 \}}\) | \(0.02666 ^{\{ 4.5 \}}\) | \(0.02882 ^{\{ 6 \}}\) | \(0.0264 ^{\{ 3 \}}\) | \(0.02994 ^{\{ 9 \}}\) | \(0.02242 ^{\{ 1 \}}\) | \(0.02952 ^{\{ 8 \}}\) | \(0.02666 ^{\{ 4.5 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.05406 ^{\{ 2 \}}\) | \(0.05879 ^{\{ 4 \}}\) | \(0.06096 ^{\{ 7 \}}\) | \(0.05958 ^{\{ 5 \}}\) | \(0.06401 ^{\{ 8 \}}\) | \(0.05042 ^{\{ 1 \}}\) | \(0.06572 ^{\{ 9 \}}\) | \(0.05843 ^{\{ 3 \}}\) | |
\(\pmb K{_4}\) | \(0.00946 ^{\{ 2 \}}\) | \(0.00953 ^{\{ 4 \}}\) | \(0.00972 ^{\{ 5 \}}\) | \(0.00978 ^{\{ 6 \}}\) | \(0.01021 ^{\{ 7 \}}\) | \(0.00927 ^{\{ 1 \}}\) | \(0.01041 ^{\{ 9 \}}\) | \(0.0095 ^{\{ 3 \}}\) | |
\(\pmb K{_5}\) | \(0.01568 ^{\{ 2 \}}\) | \(0.01612 ^{\{ 4 \}}\) | \(0.0166 ^{\{ 6 \}}\) | \(0.01651 ^{\{ 5 \}}\) | \(0.01744 ^{\{ 7 \}}\) | \(0.01551 ^{\{ 1 \}}\) | \(0.01758 ^{\{ 8 \}}\) | \(0.01608 ^{\{ 3 \}}\) | |
\(\pmb K{_6}\) | \(0.12853 ^{\{ 2 \}}\) | \(0.14192 ^{\{ 4 \}}\) | \(0.15092 ^{\{ 6 \}}\) | \(0.08588 ^{\{ 5 \}}\) | \(0.13886 ^{\{ 7 \}}\) | \(0.00852 ^{\{ 1 \}}\) | \(0.1656 ^{\{ 8 \}}\) | \(0.13348 ^{\{ 3 \}}\) | |
\(\sum Ranks\) | \(18 ^{\{ 1 \}}\) | \(41 ^{\{ 4 \}}\) | \(57.5 ^{\{ 6 \}}\) | \(47.5 ^{\{ 5 \}}\) | \(68 ^{\{ 8 \}}\) | \(24.5 ^{\{ 2 \}}\) | \(80 ^{\{ 9 \}}\) | \(32 ^{\{ 3 \}}\) | |
400 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.02535 ^{\{ 2 \}}\) | \(0.02748 ^{\{ 3 \}}\) | \(0.03061 ^{\{ 6 \}}\) | \(0.02937 ^{\{ 5 \}}\) | \(0.03224 ^{\{ 8 \}}\) | \(0.02375 ^{\{ 1 \}}\) | \(0.03135 ^{\{ 7 \}}\) | \(0.02816 ^{\{ 4 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.0138 ^{\{ 2 \}}\) | \(0.0145 ^{\{ 3 \}}\) | \(0.01588 ^{\{ 6 \}}\) | \(0.01584 ^{\{ 5 \}}\) | \(0.01669 ^{\{ 8 \}}\) | \(0.01292 ^{\{ 1 \}}\) | \(0.01691 ^{\{ 9 \}}\) | \(0.01499 ^{\{ 4 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.001 ^{\{ 1 \}}\) | \(0.00124 ^{\{ 3 \}}\) | \(0.00148 ^{\{ 6 \}}\) | \(0.00132 ^{\{ 5 \}}\) | \(0.00159 ^{\{ 8 \}}\) | \(0.00112 ^{\{ 2 \}}\) | \(0.00152 ^{\{ 7 \}}\) | \(0.00125 ^{\{ 4 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(3e-04 ^{\{ 1 \}}\) | \(0.00034 ^{\{ 2.5 \}}\) | \(4e-04 ^{\{ 5.5 \}}\) | \(4e-04 ^{\{ 5.5 \}}\) | \(0.00043 ^{\{ 8 \}}\) | \(0.00034 ^{\{ 2.5 \}}\) | \(0.00045 ^{\{ 9 \}}\) | \(0.00035 ^{\{ 4 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.02028 ^{\{ 2 \}}\) | \(0.02198 ^{\{ 3 \}}\) | \(0.02449 ^{\{ 6 \}}\) | \(0.0235 ^{\{ 5 \}}\) | \(0.0258 ^{\{ 8 \}}\) | \(0.019 ^{\{ 1 \}}\) | \(0.02508 ^{\{ 7 \}}\) | \(0.02253 ^{\{ 4 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.046 ^{\{ 2 \}}\) | \(0.04833 ^{\{ 3 \}}\) | \(0.05293 ^{\{ 6 \}}\) | \(0.05279 ^{\{ 5 \}}\) | \(0.05563 ^{\{ 8 \}}\) | \(0.04306 ^{\{ 1 \}}\) | \(0.05637 ^{\{ 9 \}}\) | \(0.04997 ^{\{ 4 \}}\) | |
\(\pmb K{_4}\) | \(0.00801 ^{\{ 2 \}}\) | \(0.00826 ^{\{ 4 \}}\) | \(0.00887 ^{\{ 7.5 \}}\) | \(0.00829 ^{\{ 5 \}}\) | \(0.00877 ^{\{ 6 \}}\) | \(0.00789 ^{\{ 1 \}}\) | \(0.00892 ^{\{ 9 \}}\) | \(0.00821 ^{\{ 3 \}}\) | |
\(\pmb K{_5}\) | \(0.01345 ^{\{ 2 \}}\) | \(0.01389 ^{\{ 3 \}}\) | \(0.01503 ^{\{ 6 \}}\) | \(0.01407 ^{\{ 5 \}}\) | \(0.01504 ^{\{ 7 \}}\) | \(0.0132 ^{\{ 1 \}}\) | \(0.01512 ^{\{ 8 \}}\) | \(0.01391 ^{\{ 4 \}}\) | |
\(\pmb K{_6}\) | \(0.1081 ^{\{ 2 \}}\) | \(0.10327 ^{\{ 3 \}}\) | \(0.12704 ^{\{ 6 \}}\) | \(0.07395 ^{\{ 5 \}}\) | \(0.1181 ^{\{ 7 \}}\) | \(0.00715 ^{\{ 1 \}}\) | \(0.13335 ^{\{ 8 \}}\) | \(0.10639 ^{\{ 4 \}}\) | |
\(\sum Ranks\) | \(34 ^{\{ 3 \}}\) | \(27.5 ^{\{ 2 \}}\) | \(68 ^{\{ 7 \}}\) | \(52.5 ^{\{ 5 \}}\) | \(66 ^{\{ 6 \}}\) | \(10.5 ^{\{ 1 \}}\) | \(74 ^{\{ 9 \}}\) | \(36 ^{\{ 4 \}}\) | |
500 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.02277 ^{\{ 2 \}}\) | \(0.02502 ^{\{ 5 \}}\) | \(0.02899 ^{\{ 8.5 \}}\) | \(0.02491 ^{\{ 4 \}}\) | \(0.02869 ^{\{ 7 \}}\) | \(0.02044 ^{\{ 1 \}}\) | \(0.02764 ^{\{ 6 \}}\) | \(0.02479 ^{\{ 3 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.01216 ^{\{ 2 \}}\) | \(0.01327 ^{\{ 4 \}}\) | \(0.01503 ^{\{ 10 \}}\) | \(0.0133 ^{\{ 5 \}}\) | \(0.01474 ^{\{ 7 \}}\) | \(0.01101 ^{\{ 1 \}}\) | \(0.01461 ^{\{ 6 \}}\) | \(0.01306 ^{\{ 3 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00081 ^{\{ 1 \}}\) | \(0.00099 ^{\{ 4 \}}\) | \(0.00131 ^{\{ 8 \}}\) | \(0.00098 ^{\{ 3 \}}\) | \(0.00128 ^{\{ 7 \}}\) | \(0.00086 ^{\{ 2 \}}\) | \(0.00121 ^{\{ 6 \}}\) | \(0.001 ^{\{ 5 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00023 ^{\{ 1 \}}\) | \(0.00028 ^{\{ 4.5 \}}\) | \(0.00035 ^{\{ 9 \}}\) | \(0.00028 ^{\{ 4.5 \}}\) | \(0.00034 ^{\{ 7 \}}\) | \(0.00026 ^{\{ 2 \}}\) | \(0.00034 ^{\{ 7 \}}\) | \(0.00027 ^{\{ 3 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.01822 ^{\{ 2 \}}\) | \(0.02001 ^{\{ 5 \}}\) | \(0.02319 ^{\{ 8.5 \}}\) | \(0.01993 ^{\{ 4 \}}\) | \(0.02295 ^{\{ 7 \}}\) | \(0.01635 ^{\{ 1 \}}\) | \(0.02211 ^{\{ 6 \}}\) | \(0.01983 ^{\{ 3 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.04055 ^{\{ 2 \}}\) | \(0.04422 ^{\{ 4 \}}\) | \(0.05009 ^{\{ 10 \}}\) | \(0.04433 ^{\{ 5 \}}\) | \(0.04912 ^{\{ 7 \}}\) | \(0.03671 ^{\{ 1 \}}\) | \(0.0487 ^{\{ 6 \}}\) | \(0.04353 ^{\{ 3 \}}\) | |
\(\pmb K{_4}\) | \(0.00675 ^{\{ 1 \}}\) | \(0.00726 ^{\{ 4 \}}\) | \(0.00794 ^{\{ 8 \}}\) | \(0.0072 ^{\{ 3 \}}\) | \(0.00771 ^{\{ 7 \}}\) | \(0.00692 ^{\{ 2 \}}\) | \(0.00767 ^{\{ 6 \}}\) | \(0.00746 ^{\{ 5 \}}\) | |
\(\pmb K{_5}\) | \(0.01137 ^{\{ 1 \}}\) | \(0.01228 ^{\{ 4 \}}\) | \(0.01351 ^{\{ 8 \}}\) | \(0.01213 ^{\{ 3 \}}\) | \(0.01319 ^{\{ 7 \}}\) | \(0.01152 ^{\{ 2 \}}\) | \(0.01305 ^{\{ 6 \}}\) | \(0.01255 ^{\{ 5 \}}\) | |
\(\pmb K{_6}\) | \(0.08507 ^{\{ 1 \}}\) | \(0.08993 ^{\{ 4 \}}\) | \(0.11044 ^{\{ 8 \}}\) | \(0.06485 ^{\{ 3 \}}\) | \(0.10595 ^{\{ 7 \}}\) | \(0.00637 ^{\{ 2 \}}\) | \(0.10808 ^{\{ 6 \}}\) | \(0.08979 ^{\{ 5 \}}\) | |
\(\sum Ranks\) | \(16 ^{\{ 2 \}}\) | \(40.5 ^{\{ 5 \}}\) | \(84 ^{\{ 9.5 \}}\) | \(33.5 ^{\{ 3 \}}\) | \(66 ^{\{ 7 \}}\) | \(13 ^{\{ 1 \}}\) | \(61 ^{\{ 6 \}}\) | \(35 ^{\{ 4 \}}\) |
n | Est. | LTADE | MSADE | MSALDE | ADSOE | KE | MSSD | MSSLD | MSLND |
|---|---|---|---|---|---|---|---|---|---|
30 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.12691 ^{\{ 12 \}}\) | \(0.13887 ^{\{ 13 \}}\) | \(0.12627 ^{\{ 9 \}}\) | \(0.18167 ^{\{ 16 \}}\) | \(0.12653 ^{\{ 10 \}}\) | \(0.16721 ^{\{ 14 \}}\) | \(0.11951 ^{\{ 7 \}}\) | \(0.17252 ^{\{ 15 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.0627 ^{\{ 9 \}}\) | \(0.08014 ^{\{ 13 \}}\) | \(0.07484 ^{\{ 12 \}}\) | \(0.08209 ^{\{ 14 \}}\) | \(0.06237 ^{\{ 7 \}}\) | \(0.09146 ^{\{ 15 \}}\) | \(0.0693 ^{\{ 11 \}}\) | \(0.09449 ^{\{ 16 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.02512 ^{\{ 10 \}}\) | \(0.0302 ^{\{ 13 \}}\) | \(0.02446 ^{\{ 8 \}}\) | \(0.05273 ^{\{ 16 \}}\) | \(0.02736 ^{\{ 12 \}}\) | \(0.04295 ^{\{ 14 \}}\) | \(0.02194 ^{\{ 6 \}}\) | \(0.04481 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00599 ^{\{ 6 \}}\) | \(0.01032 ^{\{ 13 \}}\) | \(0.00907 ^{\{ 12 \}}\) | \(0.01067 ^{\{ 14 \}}\) | \(0.00612 ^{\{ 7 \}}\) | \(0.01292 ^{\{ 15 \}}\) | \(0.00782 ^{\{ 11 \}}\) | \(0.01355 ^{\{ 16 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.10152 ^{\{ 12 \}}\) | \(0.11109 ^{\{ 13 \}}\) | \(0.10102 ^{\{ 9 \}}\) | \(0.14533 ^{\{ 16 \}}\) | \(0.10122 ^{\{ 10 \}}\) | \(0.13377 ^{\{ 14 \}}\) | \(0.09561 ^{\{ 7 \}}\) | \(0.13802 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.20899 ^{\{ 9 \}}\) | \(0.26713 ^{\{ 13 \}}\) | \(0.24945 ^{\{ 12 \}}\) | \(0.27365 ^{\{ 14 \}}\) | \(0.2079 ^{\{ 7 \}}\) | \(0.30486 ^{\{ 15 \}}\) | \(0.23099 ^{\{ 11 \}}\) | \(0.31497 ^{\{ 16 \}}\) | |
\(\pmb K{_4}\) | \(0.03334 ^{\{ 9 \}}\) | \(0.0454 ^{\{ 14 \}}\) | \(0.04176 ^{\{ 12 \}}\) | \(0.04423 ^{\{ 13 \}}\) | \(0.03437 ^{\{ 10 \}}\) | \(0.04581 ^{\{ 15 \}}\) | \(0.03608 ^{\{ 11 \}}\) | \(0.04713 ^{\{ 16 \}}\) | |
\(\pmb K{_5}\) | \(0.05713 ^{\{ 9 \}}\) | \(0.07536 ^{\{ 13 \}}\) | \(0.06987 ^{\{ 12 \}}\) | \(0.07868 ^{\{ 14 \}}\) | \(0.05881 ^{\{ 10 \}}\) | \(0.07899 ^{\{ 15 \}}\) | \(0.06064 ^{\{ 11 \}}\) | \(0.08054 ^{\{ 16 \}}\) | |
\(\pmb K{_6}\) | \(1.02465 ^{\{ 9 \}}\) | \(1.03032 ^{\{ 13 \}}\) | \(0.66627 ^{\{ 12 \}}\) | \(1.49751 ^{\{ 14 \}}\) | \(1.38903 ^{\{ 10 \}}\) | \(1.77718 ^{\{ 15 \}}\) | \(0.64579 ^{\{ 11 \}}\) | \(1.58558 ^{\{ 16 \}}\) | |
\(\sum Ranks\) | \(84 ^{\{ 10 \}}\) | \(114 ^{\{ 13 \}}\) | \(90 ^{\{ 12 \}}\) | \(131 ^{\{ 14 \}}\) | \(85 ^{\{ 11 \}}\) | \(133 ^{\{ 15 \}}\) | \(78 ^{\{ 9 \}}\) | \(140 ^{\{ 16 \}}\) | |
80 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.07599 ^{\{ 11 \}}\) | \(0.08478 ^{\{ 13 \}}\) | \(0.07941 ^{\{ 12 \}}\) | \(0.13006 ^{\{ 16 \}}\) | \(0.07443 ^{\{ 10 \}}\) | \(0.09901 ^{\{ 15 \}}\) | \(0.07362 ^{\{ 9 \}}\) | \(0.09869 ^{\{ 14 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.03803 ^{\{ 10 \}}\) | \(0.04992 ^{\{ 13 \}}\) | \(0.04458 ^{\{ 12 \}}\) | \(0.05897 ^{\{ 16 \}}\) | \(0.03769 ^{\{ 9 \}}\) | \(0.05658 ^{\{ 15 \}}\) | \(0.04199 ^{\{ 11 \}}\) | \(0.05498 ^{\{ 14 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00908 ^{\{ 11 \}}\) | \(0.0114 ^{\{ 13 \}}\) | \(0.00954 ^{\{ 12 \}}\) | \(0.02764 ^{\{ 16 \}}\) | \(0.00906 ^{\{ 10 \}}\) | \(0.01483 ^{\{ 14 \}}\) | \(0.00828 ^{\{ 8 \}}\) | \(0.01516 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00222 ^{\{ 10 \}}\) | \(0.004 ^{\{ 13 \}}\) | \(0.0032 ^{\{ 12 \}}\) | \(0.00605 ^{\{ 16 \}}\) | \(0.0022 ^{\{ 8.5 \}}\) | \(0.00504 ^{\{ 15 \}}\) | \(0.00289 ^{\{ 11 \}}\) | \(0.00488 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.06079 ^{\{ 11 \}}\) | \(0.06783 ^{\{ 13 \}}\) | \(0.06353 ^{\{ 12 \}}\) | \(0.10405 ^{\{ 16 \}}\) | \(0.05954 ^{\{ 10 \}}\) | \(0.07921 ^{\{ 15 \}}\) | \(0.0589 ^{\{ 9 \}}\) | \(0.07895 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.12678 ^{\{ 10 \}}\) | \(0.1664 ^{\{ 13 \}}\) | \(0.14861 ^{\{ 12 \}}\) | \(0.19656 ^{\{ 16 \}}\) | \(0.12562 ^{\{ 9 \}}\) | \(0.18859 ^{\{ 15 \}}\) | \(0.13997 ^{\{ 11 \}}\) | \(0.18328 ^{\{ 14 \}}\) | |
\(\pmb K{_4}\) | \(0.02022 ^{\{ 9 \}}\) | \(0.02863 ^{\{ 13 \}}\) | \(0.0252 ^{\{ 12 \}}\) | \(0.0309 ^{\{ 15 \}}\) | \(0.02126 ^{\{ 10 \}}\) | \(0.03058 ^{\{ 14 \}}\) | \(0.02309 ^{\{ 11 \}}\) | \(0.03098 ^{\{ 16 \}}\) | |
\(\pmb K{_5}\) | \(0.03459 ^{\{ 9 \}}\) | \(0.04752 ^{\{ 13 \}}\) | \(0.04237 ^{\{ 12 \}}\) | \(0.05561 ^{\{ 16 \}}\) | \(0.03601 ^{\{ 10 \}}\) | \(0.05173 ^{\{ 14 \}}\) | \(0.0387 ^{\{ 11 \}}\) | \(0.05234 ^{\{ 15 \}}\) | |
\(\pmb K{_6}\) | \(0.43041 ^{\{ 9 \}}\) | \(0.38039 ^{\{ 13 \}}\) | \(0.29607 ^{\{ 12 \}}\) | \(0.55892 ^{\{ 16 \}}\) | \(0.52846 ^{\{ 10 \}}\) | \(0.32574 ^{\{ 14 \}}\) | \(0.30886 ^{\{ 11 \}}\) | \(0.38154 ^{\{ 15 \}}\) | |
\(\sum Ranks\) | \(94 ^{\{ 11 \}}\) | \(113 ^{\{ 13 \}}\) | \(99 ^{\{ 12 \}}\) | \(143 ^{\{ 16 \}}\) | \(91.5 ^{\{ 10 \}}\) | \(122 ^{\{ 14 \}}\) | \(85 ^{\{ 9 \}}\) | \(126 ^{\{ 15 \}}\) | |
150 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.05544 ^{\{ 10 \}}\) | \(0.06299 ^{\{ 13 \}}\) | \(0.05638 ^{\{ 12 \}}\) | \(0.10032 ^{\{ 16 \}}\) | \(0.05452 ^{\{ 9 \}}\) | \(0.06957 ^{\{ 14 \}}\) | \(0.05597 ^{\{ 11 \}}\) | \(0.07267 ^{\{ 15 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.0274 ^{\{ 8 \}}\) | \(0.03506 ^{\{ 13 \}}\) | \(0.03287 ^{\{ 12 \}}\) | \(0.04328 ^{\{ 16 \}}\) | \(0.02827 ^{\{ 10 \}}\) | \(0.04025 ^{\{ 14 \}}\) | \(0.03122 ^{\{ 11 \}}\) | \(0.04111 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00481 ^{\{ 10 \}}\) | \(0.00625 ^{\{ 13 \}}\) | \(0.00503 ^{\{ 12 \}}\) | \(0.01676 ^{\{ 16 \}}\) | \(0.00472 ^{\{ 9 \}}\) | \(0.00734 ^{\{ 14 \}}\) | \(0.00497 ^{\{ 11 \}}\) | \(0.00805 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00115 ^{\{ 8 \}}\) | \(0.00201 ^{\{ 13 \}}\) | \(0.00176 ^{\{ 12 \}}\) | \(0.00331 ^{\{ 16 \}}\) | \(0.00127 ^{\{ 10 \}}\) | \(0.00255 ^{\{ 14 \}}\) | \(0.0016 ^{\{ 11 \}}\) | \(0.00267 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.04435 ^{\{ 10 \}}\) | \(0.0504 ^{\{ 13 \}}\) | \(0.04511 ^{\{ 12 \}}\) | \(0.08025 ^{\{ 16 \}}\) | \(0.04362 ^{\{ 9 \}}\) | \(0.05565 ^{\{ 14 \}}\) | \(0.04477 ^{\{ 11 \}}\) | \(0.05813 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.09134 ^{\{ 8 \}}\) | \(0.11688 ^{\{ 13 \}}\) | \(0.10957 ^{\{ 12 \}}\) | \(0.14428 ^{\{ 16 \}}\) | \(0.09422 ^{\{ 10 \}}\) | \(0.13416 ^{\{ 14 \}}\) | \(0.10407 ^{\{ 11 \}}\) | \(0.13702 ^{\{ 15 \}}\) | |
\(\pmb K{_4}\) | \(0.01489 ^{\{ 9 \}}\) | \(0.02129 ^{\{ 13 \}}\) | \(0.01901 ^{\{ 12 \}}\) | \(0.02396 ^{\{ 16 \}}\) | \(0.01498 ^{\{ 10 \}}\) | \(0.02261 ^{\{ 14 \}}\) | \(0.01745 ^{\{ 11 \}}\) | \(0.02329 ^{\{ 15 \}}\) | |
\(\pmb K{_5}\) | \(0.02543 ^{\{ 9 \}}\) | \(0.03557 ^{\{ 13 \}}\) | \(0.0316 ^{\{ 12 \}}\) | \(0.04385 ^{\{ 16 \}}\) | \(0.0256 ^{\{ 10 \}}\) | \(0.03779 ^{\{ 14 \}}\) | \(0.02935 ^{\{ 11 \}}\) | \(0.03902 ^{\{ 15 \}}\) | |
\(\pmb K{_6}\) | \(0.26926 ^{\{ 9 \}}\) | \(0.24718 ^{\{ 13 \}}\) | \(0.19575 ^{\{ 12 \}}\) | \(0.35369 ^{\{ 16 \}}\) | \(0.27752 ^{\{ 10 \}}\) | \(0.2063 ^{\{ 14 \}}\) | \(0.21155 ^{\{ 11 \}}\) | \(0.231 ^{\{ 15 \}}\) | |
\(\sum Ranks\) | \(85 ^{\{ 9 \}}\) | \(114 ^{\{ 13 \}}\) | \(98 ^{\{ 12 \}}\) | \(143 ^{\{ 16 \}}\) | \(91 ^{\{ 10 \}}\) | \(115 ^{\{ 14 \}}\) | \(92 ^{\{ 11 \}}\) | \(127 ^{\{ 15 \}}\) |
300 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.03679 ^{\{ 7 \}}\) | \(0.04565 ^{\{ 13 \}}\) | \(0.03957 ^{\{ 11 \}}\) | \(0.07454 ^{\{ 16 \}}\) | \(0.04026 ^{\{ 12 \}}\) | \(0.04858 ^{\{ 14 \}}\) | \(0.03923 ^{\{ 10 \}}\) | \(0.04899 ^{\{ 15 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.01813 ^{\{ 6 \}}\) | \(0.02529 ^{\{ 13 \}}\) | \(0.02244 ^{\{ 12 \}}\) | \(0.03196 ^{\{ 16 \}}\) | \(0.0207 ^{\{ 10 \}}\) | \(0.02778 ^{\{ 15 \}}\) | \(0.0217 ^{\{ 11 \}}\) | \(0.02753 ^{\{ 14 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00216 ^{\{ 8 \}}\) | \(0.00323 ^{\{ 13 \}}\) | \(0.00249 ^{\{ 11 \}}\) | \(0.00958 ^{\{ 16 \}}\) | \(0.00295 ^{\{ 12 \}}\) | \(0.00361 ^{\{ 14 \}}\) | \(0.00236 ^{\{ 10 \}}\) | \(0.00378 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00053 ^{\{ 6.5 \}}\) | \(0.00101 ^{\{ 13 \}}\) | \(0.00082 ^{\{ 12 \}}\) | \(0.00182 ^{\{ 16 \}}\) | \(0.00079 ^{\{ 11 \}}\) | \(0.00123 ^{\{ 15 \}}\) | \(0.00075 ^{\{ 10 \}}\) | \(0.00122 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.02943 ^{\{ 7 \}}\) | \(0.03652 ^{\{ 13 \}}\) | \(0.03166 ^{\{ 11 \}}\) | \(0.05963 ^{\{ 16 \}}\) | \(0.03221 ^{\{ 12 \}}\) | \(0.03886 ^{\{ 14 \}}\) | \(0.03138 ^{\{ 10 \}}\) | \(0.03919 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.06045 ^{\{ 6 \}}\) | \(0.08428 ^{\{ 13 \}}\) | \(0.0748 ^{\{ 12 \}}\) | \(0.10653 ^{\{ 16 \}}\) | \(0.069 ^{\{ 10 \}}\) | \(0.09259 ^{\{ 15 \}}\) | \(0.07235 ^{\{ 11 \}}\) | \(0.09176 ^{\{ 14 \}}\) | |
\(\pmb K{_4}\) | \(0.01036 ^{\{ 8 \}}\) | \(0.01486 ^{\{ 13 \}}\) | \(0.01332 ^{\{ 12 \}}\) | \(0.01794 ^{\{ 16 \}}\) | \(0.01094 ^{\{ 10 \}}\) | \(0.0165 ^{\{ 14 \}}\) | \(0.01224 ^{\{ 11 \}}\) | \(0.01702 ^{\{ 15 \}}\) | |
\(\pmb K{_5}\) | \(0.01774 ^{\{ 9 \}}\) | \(0.02489 ^{\{ 13 \}}\) | \(0.02215 ^{\{ 12 \}}\) | \(0.03289 ^{\{ 16 \}}\) | \(0.01866 ^{\{ 10 \}}\) | \(0.02729 ^{\{ 14 \}}\) | \(0.02055 ^{\{ 11 \}}\) | \(0.02828 ^{\{ 15 \}}\) | |
\(\pmb K{_6}\) | \(0.15238 ^{\{ 9 \}}\) | \(0.17751 ^{\{ 13 \}}\) | \(0.13756 ^{\{ 12 \}}\) | \(0.21519 ^{\{ 16 \}}\) | \(0.18933 ^{\{ 10 \}}\) | \(0.14859 ^{\{ 14 \}}\) | \(0.11866 ^{\{ 11 \}}\) | \(0.15355 ^{\{ 15 \}}\) | |
\(\sum Ranks\) | \(66.5 ^{\{ 7 \}}\) | \(116 ^{\{ 13 \}}\) | \(97 ^{\{ 11 \}}\) | \(142 ^{\{ 16 \}}\) | \(100 ^{\{ 12 \}}\) | \(122 ^{\{ 14 \}}\) | \(85 ^{\{ 10 \}}\) | \(127 ^{\{ 15 \}}\) | |
400 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.03293 ^{\{ 9 \}}\) | \(0.03917 ^{\{ 13 \}}\) | \(0.03388 ^{\{ 11 \}}\) | \(0.06423 ^{\{ 16 \}}\) | \(0.03325 ^{\{ 10 \}}\) | \(0.04381 ^{\{ 15 \}}\) | \(0.03391 ^{\{ 12 \}}\) | \(0.04357 ^{\{ 14 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.01645 ^{\{ 7 \}}\) | \(0.02191 ^{\{ 13 \}}\) | \(0.01909 ^{\{ 12 \}}\) | \(0.02708 ^{\{ 16 \}}\) | \(0.01723 ^{\{ 10 \}}\) | \(0.0249 ^{\{ 15 \}}\) | \(0.01872 ^{\{ 11 \}}\) | \(0.02476 ^{\{ 14 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00172 ^{\{ 9 \}}\) | \(0.00232 ^{\{ 13 \}}\) | \(0.00185 ^{\{ 11 \}}\) | \(0.00702 ^{\{ 16 \}}\) | \(0.00197 ^{\{ 12 \}}\) | \(0.00297 ^{\{ 14 \}}\) | \(0.00179 ^{\{ 10 \}}\) | \(0.00309 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00042 ^{\{ 7 \}}\) | \(0.00073 ^{\{ 13 \}}\) | \(0.00059 ^{\{ 12 \}}\) | \(0.00128 ^{\{ 16 \}}\) | \(0.00054 ^{\{ 10 \}}\) | \(0.00098 ^{\{ 14 \}}\) | \(0.00056 ^{\{ 11 \}}\) | \(0.00102 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.02634 ^{\{ 9 \}}\) | \(0.03134 ^{\{ 13 \}}\) | \(0.0271 ^{\{ 11 \}}\) | \(0.05139 ^{\{ 16 \}}\) | \(0.0266 ^{\{ 10 \}}\) | \(0.03505 ^{\{ 15 \}}\) | \(0.02713 ^{\{ 12 \}}\) | \(0.03486 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.05484 ^{\{ 7 \}}\) | \(0.07303 ^{\{ 13 \}}\) | \(0.06363 ^{\{ 12 \}}\) | \(0.09028 ^{\{ 16 \}}\) | \(0.05743 ^{\{ 10 \}}\) | \(0.08298 ^{\{ 15 \}}\) | \(0.06241 ^{\{ 11 \}}\) | \(0.08255 ^{\{ 14 \}}\) | |
\(\pmb K{_4}\) | \(0.00887 ^{\{ 7.5 \}}\) | \(0.01306 ^{\{ 13 \}}\) | \(0.01125 ^{\{ 12 \}}\) | \(0.01521 ^{\{ 16 \}}\) | \(0.00952 ^{\{ 10 \}}\) | \(0.01515 ^{\{ 15 \}}\) | \(0.0104 ^{\{ 11 \}}\) | \(0.01497 ^{\{ 14 \}}\) | |
\(\pmb K{_5}\) | \(0.01523 ^{\{ 9 \}}\) | \(0.02176 ^{\{ 13 \}}\) | \(0.01871 ^{\{ 12 \}}\) | \(0.02788 ^{\{ 16 \}}\) | \(0.01609 ^{\{ 10 \}}\) | \(0.02501 ^{\{ 15 \}}\) | \(0.01749 ^{\{ 11 \}}\) | \(0.02479 ^{\{ 14 \}}\) | |
\(\pmb K{_6}\) | \(0.12771 ^{\{ 9 \}}\) | \(0.14703 ^{\{ 13 \}}\) | \(0.105 ^{\{ 12 \}}\) | \(0.18019 ^{\{ 16 \}}\) | \(0.14066 ^{\{ 10 \}}\) | \(0.12736 ^{\{ 15 \}}\) | \(0.09451 ^{\{ 11 \}}\) | \(0.14567 ^{\{ 14 \}}\) | |
\(\sum Ranks\) | \(72.5 ^{\{ 8 \}}\) | \(116 ^{\{ 13 \}}\) | \(95 ^{\{ 12 \}}\) | \(141 ^{\{ 16 \}}\) | \(92 ^{\{ 11 \}}\) | \(125 ^{\{ 14.5 \}}\) | \(89 ^{\{ 10 \}}\) | \(125 ^{\{ 14.5 \}}\) | |
500 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.02936 ^{\{ 10 \}}\) | \(0.03471 ^{\{ 13 \}}\) | \(0.03083 ^{\{ 12 \}}\) | \(0.05641 ^{\{ 16 \}}\) | \(0.02899 ^{\{ 8.5 \}}\) | \(0.03806 ^{\{ 14 \}}\) | \(0.02968 ^{\{ 11 \}}\) | \(0.03896 ^{\{ 15 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.01491 ^{\{ 8 \}}\) | \(0.01977 ^{\{ 13 \}}\) | \(0.01713 ^{\{ 12 \}}\) | \(0.02377 ^{\{ 16 \}}\) | \(0.01501 ^{\{ 9 \}}\) | \(0.02156 ^{\{ 14 \}}\) | \(0.0165 ^{\{ 11 \}}\) | \(0.02229 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00135 ^{\{ 9 \}}\) | \(0.00192 ^{\{ 13 \}}\) | \(0.00146 ^{\{ 12 \}}\) | \(0.00581 ^{\{ 16 \}}\) | \(0.00142 ^{\{ 11 \}}\) | \(0.00227 ^{\{ 14 \}}\) | \(0.00141 ^{\{ 10 \}}\) | \(0.00233 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00034 ^{\{ 7 \}}\) | \(0.00061 ^{\{ 13 \}}\) | \(0.00047 ^{\{ 12 \}}\) | \(0.00106 ^{\{ 16 \}}\) | \(0.00039 ^{\{ 10 \}}\) | \(0.00074 ^{\{ 14 \}}\) | \(0.00044 ^{\{ 11 \}}\) | \(0.00077 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.02349 ^{\{ 10 \}}\) | \(0.02777 ^{\{ 13 \}}\) | \(0.02466 ^{\{ 12 \}}\) | \(0.04513 ^{\{ 16 \}}\) | \(0.02319 ^{\{ 8.5 \}}\) | \(0.03045 ^{\{ 14 \}}\) | \(0.02374 ^{\{ 11 \}}\) | \(0.03117 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.04969 ^{\{ 8 \}}\) | \(0.06589 ^{\{ 13 \}}\) | \(0.05708 ^{\{ 12 \}}\) | \(0.07922 ^{\{ 16 \}}\) | \(0.05002 ^{\{ 9 \}}\) | \(0.07188 ^{\{ 14 \}}\) | \(0.05502 ^{\{ 11 \}}\) | \(0.0743 ^{\{ 15 \}}\) | |
\(\pmb K{_4}\) | \(0.00807 ^{\{ 9 \}}\) | \(0.01149 ^{\{ 13 \}}\) | \(0.01005 ^{\{ 12 \}}\) | \(0.01357 ^{\{ 16 \}}\) | \(0.00819 ^{\{ 10 \}}\) | \(0.01318 ^{\{ 15 \}}\) | \(0.0094 ^{\{ 11 \}}\) | \(0.01314 ^{\{ 14 \}}\) | |
\(\pmb K{_5}\) | \(0.0138 ^{\{ 9 \}}\) | \(0.0191 ^{\{ 13 \}}\) | \(0.01672 ^{\{ 12 \}}\) | \(0.02485 ^{\{ 16 \}}\) | \(0.01391 ^{\{ 10 \}}\) | \(0.02177 ^{\{ 14 \}}\) | \(0.01576 ^{\{ 11 \}}\) | \(0.02179 ^{\{ 15 \}}\) | |
\(\pmb K{_6}\) | \(0.10562 ^{\{ 9 \}}\) | \(0.11797 ^{\{ 13 \}}\) | \(0.09213 ^{\{ 12 \}}\) | \(0.15007 ^{\{ 16 \}}\) | \(0.10523 ^{\{ 10 \}}\) | \(0.1071 ^{\{ 14 \}}\) | \(0.08258 ^{\{ 11 \}}\) | \(0.10819 ^{\{ 15 \}}\) | |
\(\sum Ranks\) | \(79 ^{\{ 8 \}}\) | \(119 ^{\{ 13 \}}\) | \(103 ^{\{ 12 \}}\) | \(144 ^{\{ 16 \}}\) | \(84 ^{\{ 9.5 \}}\) | \(124 ^{\{ 14 \}}\) | \(90 ^{\{ 11 \}}\) | \(132 ^{\{ 15 \}}\) |
