Table 2 Numerical values of simulation measures for \(\alpha =1.5,~\beta =2.0\) under RSS.
n | Est. | MLE | ADE | CVME | MPSE | OLSE | PCE | RTADE | WLSE |
|---|---|---|---|---|---|---|---|---|---|
30 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.13546 ^{\{ 1 \}}\) | \(0.1606 ^{\{ 2 \}}\) | \(0.17903 ^{\{ 9 \}}\) | \(0.17242 ^{\{ 7 \}}\) | \(0.17842 ^{\{ 8 \}}\) | \(0.16665 ^{\{ 6 \}}\) | \(0.16449 ^{\{ 5 \}}\) | \(0.16064 ^{\{ 3 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.12514 ^{\{ 4 \}}\) | \(0.12804 ^{\{ 5 \}}\) | \(0.13453 ^{\{ 8 \}}\) | \(0.12307 ^{\{ 2 \}}\) | \(0.12961 ^{\{ 6 \}}\) | \(0.12375 ^{\{ 3 \}}\) | \(0.13166 ^{\{ 7 \}}\) | \(0.12016 ^{\{ 1 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.03089 ^{\{ 1 \}}\) | \(0.04041 ^{\{ 2 \}}\) | \(0.05533 ^{\{ 10 \}}\) | \(0.04328 ^{\{ 6 \}}\) | \(0.05039 ^{\{ 8 \}}\) | \(0.04092 ^{\{ 4 \}}\) | \(0.04563 ^{\{ 7 \}}\) | \(0.04197 ^{\{ 5 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.02504 ^{\{ 4 \}}\) | \(0.02634 ^{\{ 5 \}}\) | \(0.03234 ^{\{ 8 \}}\) | \(0.02362 ^{\{ 2 \}}\) | \(0.02663 ^{\{ 6 \}}\) | \(0.02401 ^{\{ 3 \}}\) | \(0.02847 ^{\{ 7 \}}\) | \(0.02331 ^{\{ 1 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.09031 ^{\{ 1 \}}\) | \(0.10707 ^{\{ 2 \}}\) | \(0.11935 ^{\{ 9 \}}\) | \(0.11494 ^{\{ 7 \}}\) | \(0.11894 ^{\{ 8 \}}\) | \(0.1111 ^{\{ 6 \}}\) | \(0.10966 ^{\{ 5 \}}\) | \(0.10709 ^{\{ 3 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.06257 ^{\{ 4 \}}\) | \(0.06402 ^{\{ 5 \}}\) | \(0.06726 ^{\{ 8 \}}\) | \(0.06154 ^{\{ 2 \}}\) | \(0.0648 ^{\{ 6 \}}\) | \(0.06188 ^{\{ 3 \}}\) | \(0.06583 ^{\{ 7 \}}\) | \(0.06008 ^{\{ 1 \}}\) | |
\(\pmb K{_4}\) | \(0.02786 ^{\{ 1 \}}\) | \(0.0305 ^{\{ 3 \}}\) | \(0.03185 ^{\{ 7 \}}\) | \(0.03181 ^{\{ 6 \}}\) | \(0.03262 ^{\{ 8 \}}\) | \(0.03116 ^{\{ 5 \}}\) | \(0.03103 ^{\{ 4 \}}\) | \(0.02987 ^{\{ 2 \}}\) | |
\(\pmb K{_5}\) | \(0.04589 ^{\{ 1 \}}\) | \(0.05124 ^{\{ 3 \}}\) | \(0.05406 ^{\{ 7 \}}\) | \(0.05375 ^{\{ 6 \}}\) | \(0.05501 ^{\{ 8 \}}\) | \(0.05306 ^{\{ 5 \}}\) | \(0.05176 ^{\{ 4 \}}\) | \(0.05004 ^{\{ 2 \}}\) | |
\(\pmb K{_6}\) | \(0.05159 ^{\{ 1 \}}\) | \(0.05286 ^{\{ 3 \}}\) | \(0.07337 ^{\{ 7 \}}\) | \(0.04216 ^{\{ 6 \}}\) | \(0.05543 ^{\{ 8 \}}\) | \(0.03071 ^{\{ 5 \}}\) | \(0.06896 ^{\{ 4 \}}\) | \(0.05039 ^{\{ 2 \}}\) | |
\(\sum Ranks\) | \(22 ^{\{ 1.5 \}}\) | \(33 ^{\{ 3 \}}\) | \(77 ^{\{ 9 \}}\) | \(40 ^{\{ 5 \}}\) | \(65 ^{\{ 7 \}}\) | \(36 ^{\{ 4 \}}\) | \(56 ^{\{ 6 \}}\) | \(22 ^{\{ 1.5 \}}\) | |
80 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.08245 ^{\{ 1 \}}\) | \(0.09193 ^{\{ 2 \}}\) | \(0.10714 ^{\{ 9 \}}\) | \(0.10163 ^{\{ 6 \}}\) | \(0.1056 ^{\{ 8 \}}\) | \(0.10326 ^{\{ 7 \}}\) | \(0.0949 ^{\{ 4 \}}\) | \(0.09439 ^{\{ 3 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.08175 ^{\{ 8 \}}\) | \(0.07801 ^{\{ 3 \}}\) | \(0.0802 ^{\{ 6 \}}\) | \(0.0784 ^{\{ 4 \}}\) | \(0.07676 ^{\{ 2 \}}\) | \(0.07447 ^{\{ 1 \}}\) | \(0.08262 ^{\{ 9 \}}\) | \(0.07845 ^{\{ 5 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.01051 ^{\{ 1 \}}\) | \(0.01374 ^{\{ 2 \}}\) | \(0.01845 ^{\{ 9 \}}\) | \(0.01489 ^{\{ 5 \}}\) | \(0.01738 ^{\{ 8 \}}\) | \(0.01635 ^{\{ 7 \}}\) | \(0.01407 ^{\{ 4 \}}\) | \(0.01401 ^{\{ 3 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.01045 ^{\{ 7 \}}\) | \(0.00941 ^{\{ 2 \}}\) | \(0.01019 ^{\{ 6 \}}\) | \(0.00975 ^{\{ 5 \}}\) | \(0.00946 ^{\{ 3 \}}\) | \(0.00889 ^{\{ 1 \}}\) | \(0.01063 ^{\{ 8 \}}\) | \(0.00957 ^{\{ 4 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.05497 ^{\{ 1 \}}\) | \(0.06129 ^{\{ 2 \}}\) | \(0.07143 ^{\{ 9 \}}\) | \(0.06775 ^{\{ 6 \}}\) | \(0.0704 ^{\{ 8 \}}\) | \(0.06884 ^{\{ 7 \}}\) | \(0.06327 ^{\{ 4 \}}\) | \(0.06293 ^{\{ 3 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.04088 ^{\{ 8 \}}\) | \(0.03901 ^{\{ 3 \}}\) | \(0.0401 ^{\{ 6 \}}\) | \(0.0392 ^{\{ 4 \}}\) | \(0.03838 ^{\{ 2 \}}\) | \(0.03723 ^{\{ 1 \}}\) | \(0.04131 ^{\{ 9 \}}\) | \(0.03922 ^{\{ 5 \}}\) | |
\(\pmb K{_4}\) | \(0.01788 ^{\{ 1 \}}\) | \(0.01829 ^{\{ 2 \}}\) | \(0.01934 ^{\{ 7 \}}\) | \(0.01941 ^{\{ 8 \}}\) | \(0.01909 ^{\{ 6 \}}\) | \(0.01908 ^{\{ 5 \}}\) | \(0.01905 ^{\{ 4 \}}\) | \(0.01843 ^{\{ 3 \}}\) | |
\(\pmb K{_5}\) | \(0.02966 ^{\{ 1 \}}\) | \(0.03059 ^{\{ 2 \}}\) | \(0.0328 ^{\{ 8 \}}\) | \(0.03262 ^{\{ 7 \}}\) | \(0.03235 ^{\{ 6 \}}\) | \(0.03187 ^{\{ 5 \}}\) | \(0.03169 ^{\{ 4 \}}\) | \(0.03112 ^{\{ 3 \}}\) | |
\(\pmb K{_6}\) | \(0.01887 ^{\{ 1 \}}\) | \(0.01803 ^{\{ 2 \}}\) | \(0.02026 ^{\{ 8 \}}\) | \(0.01843 ^{\{ 7 \}}\) | \(0.01841 ^{\{ 6 \}}\) | \(0.01777 ^{\{ 5 \}}\) | \(0.01778 ^{\{ 4 \}}\) | \(0.01739 ^{\{ 3 \}}\) | |
\(\sum Ranks\) | \(35 ^{\{ 3 \}}\) | \(22 ^{\{ 1 \}}\) | \(68 ^{\{ 8 \}}\) | \(51 ^{\{ 7 \}}\) | \(48 ^{\{ 5 \}}\) | \(36 ^{\{ 4 \}}\) | \(49 ^{\{ 6 \}}\) | \(30 ^{\{ 2 \}}\) | |
150 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.06108 ^{\{ 1 \}}\) | \(0.06867 ^{\{ 3 \}}\) | \(0.0768 ^{\{ 8 \}}\) | \(0.07026 ^{\{ 4 \}}\) | \(0.07867 ^{\{ 10 \}}\) | \(0.07418 ^{\{ 5 \}}\) | \(0.07503 ^{\{ 6 \}}\) | \(0.0668 ^{\{ 2 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.05891 ^{\{ 7 \}}\) | \(0.05745 ^{\{ 6 \}}\) | \(0.06151 ^{\{ 9 \}}\) | \(0.05495 ^{\{ 2 \}}\) | \(0.05604 ^{\{ 3 \}}\) | \(0.05482 ^{\{ 1 \}}\) | \(0.05646 ^{\{ 4 \}}\) | \(0.05681 ^{\{ 5 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00598 ^{\{ 1 \}}\) | \(0.00728 ^{\{ 3 \}}\) | \(0.00953 ^{\{ 8 \}}\) | \(0.00773 ^{\{ 4 \}}\) | \(0.00964 ^{\{ 9 \}}\) | \(0.00855 ^{\{ 5 \}}\) | \(0.00885 ^{\{ 7 \}}\) | \(0.00702 ^{\{ 2 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00541 ^{\{ 7 \}}\) | \(0.00515 ^{\{ 5 \}}\) | \(0.00624 ^{\{ 9 \}}\) | \(0.00484 ^{\{ 2 \}}\) | \(0.00485 ^{\{ 3 \}}\) | \(0.00472 ^{\{ 1 \}}\) | \(0.00494 ^{\{ 4 \}}\) | \(0.00517 ^{\{ 6 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.04072 ^{\{ 1 \}}\) | \(0.04578 ^{\{ 3 \}}\) | \(0.0512 ^{\{ 8 \}}\) | \(0.04684 ^{\{ 4 \}}\) | \(0.05244 ^{\{ 10 \}}\) | \(0.04946 ^{\{ 5 \}}\) | \(0.05002 ^{\{ 6 \}}\) | \(0.04453 ^{\{ 2 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.02946 ^{\{ 7 \}}\) | \(0.02873 ^{\{ 6 \}}\) | \(0.03075 ^{\{ 9 \}}\) | \(0.02748 ^{\{ 2 \}}\) | \(0.02802 ^{\{ 3 \}}\) | \(0.02741 ^{\{ 1 \}}\) | \(0.02823 ^{\{ 4 \}}\) | \(0.02841 ^{\{ 5 \}}\) | |
\(\pmb K{_4}\) | \(0.01316 ^{\{ 1 \}}\) | \(0.01353 ^{\{ 4 \}}\) | \(0.01471 ^{\{ 8.5 \}}\) | \(0.01347 ^{\{ 3 \}}\) | \(0.01406 ^{\{ 7 \}}\) | \(0.01357 ^{\{ 5 \}}\) | \(0.01387 ^{\{ 6 \}}\) | \(0.01332 ^{\{ 2 \}}\) | |
\(\pmb K{_5}\) | \(0.02187 ^{\{ 1 \}}\) | \(0.02269 ^{\{ 4 \}}\) | \(0.0247 ^{\{ 8 \}}\) | \(0.02256 ^{\{ 3 \}}\) | \(0.02393 ^{\{ 7 \}}\) | \(0.02297 ^{\{ 5 \}}\) | \(0.02312 ^{\{ 6 \}}\) | \(0.02223 ^{\{ 2 \}}\) | |
\(\pmb K{_6}\) | \(0.0128 ^{\{ 1 \}}\) | \(0.01205 ^{\{ 4 \}}\) | \(0.01242 ^{\{ 8 \}}\) | \(0.01267 ^{\{ 3 \}}\) | \(0.01228 ^{\{ 7 \}}\) | \(0.01243 ^{\{ 5 \}}\) | \(0.01239 ^{\{ 6 \}}\) | \(0.01222 ^{\{ 2 \}}\) | |
\(\sum Ranks\) | \(34 ^{\{ 3.5 \}}\) | \(35 ^{\{ 5 \}}\) | \(72.5 ^{\{ 8 \}}\) | \(31 ^{\{ 2 \}}\) | \(55 ^{\{ 7 \}}\) | \(34 ^{\{ 3.5 \}}\) | \(47 ^{\{ 6 \}}\) | \(28 ^{\{ 1 \}}\) | |
300 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.04104 ^{\{ 1 \}}\) | \(0.04887 ^{\{ 3 \}}\) | \(0.05507 ^{\{ 9 \}}\) | \(0.04941 ^{\{ 4 \}}\) | \(0.05413 ^{\{ 8 \}}\) | \(0.05346 ^{\{ 6 \}}\) | \(0.05064 ^{\{ 5 \}}\) | \(0.04696 ^{\{ 2 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.04093 ^{\{ 6 \}}\) | \(0.04022 ^{\{ 3 \}}\) | \(0.04406 ^{\{ 9 \}}\) | \(0.04124 ^{\{ 7 \}}\) | \(0.04052 ^{\{ 5 \}}\) | \(0.03931 ^{\{ 1 \}}\) | \(0.04045 ^{\{ 4 \}}\) | \(0.03988 ^{\{ 2 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00262 ^{\{ 1 \}}\) | \(0.00361 ^{\{ 3 \}}\) | \(0.0048 ^{\{ 9 \}}\) | \(0.00365 ^{\{ 4 \}}\) | \(0.00452 ^{\{ 7 \}}\) | \(0.00441 ^{\{ 6 \}}\) | \(0.00392 ^{\{ 5 \}}\) | \(0.00348 ^{\{ 2 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00266 ^{\{ 6.5 \}}\) | \(0.00253 ^{\{ 2 \}}\) | \(0.00305 ^{\{ 9 \}}\) | \(0.00266 ^{\{ 6.5 \}}\) | \(0.00254 ^{\{ 3.5 \}}\) | \(0.00244 ^{\{ 1 \}}\) | \(0.00259 ^{\{ 5 \}}\) | \(0.00254 ^{\{ 3.5 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.02736 ^{\{ 1 \}}\) | \(0.03258 ^{\{ 3 \}}\) | \(0.03671 ^{\{ 9 \}}\) | \(0.03294 ^{\{ 4 \}}\) | \(0.03608 ^{\{ 8 \}}\) | \(0.03564 ^{\{ 6 \}}\) | \(0.03376 ^{\{ 5 \}}\) | \(0.03131 ^{\{ 2 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.02047 ^{\{ 6 \}}\) | \(0.02011 ^{\{ 3 \}}\) | \(0.02203 ^{\{ 9 \}}\) | \(0.02062 ^{\{ 7 \}}\) | \(0.02026 ^{\{ 5 \}}\) | \(0.01965 ^{\{ 1 \}}\) | \(0.02022 ^{\{ 4 \}}\) | \(0.01994 ^{\{ 2 \}}\) | |
\(\pmb K{_4}\) | \(0.00904 ^{\{ 1 \}}\) | \(0.00947 ^{\{ 3 \}}\) | \(0.01056 ^{\{ 9 \}}\) | \(0.00981 ^{\{ 5 \}}\) | \(0.00983 ^{\{ 7 \}}\) | \(0.00982 ^{\{ 6 \}}\) | \(0.00967 ^{\{ 4 \}}\) | \(0.00932 ^{\{ 2 \}}\) | |
\(\pmb K{_5}\) | \(0.01498 ^{\{ 1 \}}\) | \(0.01592 ^{\{ 3 \}}\) | \(0.01779 ^{\{ 9 \}}\) | \(0.01636 ^{\{ 5 \}}\) | \(0.01675 ^{\{ 7 \}}\) | \(0.01648 ^{\{ 6 \}}\) | \(0.01618 ^{\{ 4 \}}\) | \(0.01566 ^{\{ 2 \}}\) | |
\(\pmb K{_6}\) | \(0.00848 ^{\{ 1 \}}\) | \(0.00811 ^{\{ 3 \}}\) | \(0.00844 ^{\{ 9 \}}\) | \(0.00851 ^{\{ 5 \}}\) | \(0.00833 ^{\{ 7 \}}\) | \(0.00836 ^{\{ 6 \}}\) | \(0.00797 ^{\{ 4 \}}\) | \(0.00804 ^{\{ 2 \}}\) | |
\(\sum Ranks\) | \(30.5 ^{\{ 3 \}}\) | \(26 ^{\{ 2 \}}\) | \(78 ^{\{ 8 \}}\) | \(50.5 ^{\{ 6 \}}\) | \(54.5 ^{\{ 7 \}}\) | \(38 ^{\{ 5 \}}\) | \(37 ^{\{ 4 \}}\) | \(19.5 ^{\{ 1 \}}\) |
400 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.03539 ^{\{ 1 \}}\) | \(0.04059 ^{\{ 2 \}}\) | \(0.04543 ^{\{ 7 \}}\) | \(0.04088 ^{\{ 3 \}}\) | \(0.04657^{\{ 8 \}}\) | \(0.04474 ^{\{ 6 \}}\) | \(0.04343 ^{\{ 5 \}}\) | \(0.04135^{\{ 4 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.0347 ^{\{ 3 \}}\) | \(0.03509 ^{\{ 4 \}}\) | \(0.03749 ^{\{ 8 \}}\) | \(0.03407 ^{\{ 2 \}}\) | \(0.03518 ^{\{ 5 \}}\) | \(0.03391 ^{\{ 1 \}}\) | \(0.0376 ^{\{ 9 \}}\) | \(0.03626 ^{\{ 6 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00192 ^{\{ 1 \}}\) | \(0.00256 ^{\{ 2.5 \}}\) | \(0.00339 ^{\{ 8 \}}\) | \(0.00256 ^{\{ 2.5 \}}\) | \(0.00335 ^{\{ 7 \}}\) | \(0.00313 ^{\{ 6 \}}\) | \(0.00309 ^{\{ 5 \}}\) | \(0.00269 ^{\{ 4 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00192 ^{\{ 3 \}}\) | \(0.00196 ^{\{ 5 \}}\) | \(0.00216 ^{\{ 8 \}}\) | \(0.00186 ^{\{ 2 \}}\) | \(0.00194 ^{\{ 4 \}}\) | \(0.00181 ^{\{ 1 \}}\) | \(0.00221 ^{\{ 9 \}}\) | \(0.0021 ^{\{ 7 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.02359 ^{\{ 1 \}}\) | \(0.02706 ^{\{ 2 \}}\) | \(0.03029 ^{\{ 7 \}}\) | \(0.02726 ^{\{ 3 \}}\) | \(0.03104 ^{\{ 8 \}}\) | \(0.02982 ^{\{ 6 \}}\) | \(0.02896 ^{\{ 5 \}}\) | \(0.02757 ^{\{ 4 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.01735 ^{\{ 3 \}}\) | \(0.01754 ^{\{ 4 \}}\) | \(0.01875 ^{\{ 8 \}}\) | \(0.01703 ^{\{ 2 \}}\) | \(0.01759 ^{\{ 5 \}}\) | \(0.01695 ^{\{ 1 \}}\) | \(0.0188 ^{\{ 9 \}}\) | \(0.01813 ^{\{ 6 \}}\) | |
\(\pmb K{_4}\) | \(0.00776 ^{\{ 1 \}}\) | \(0.0082 ^{\{ 3 \}}\) | \(0.00883 ^{\{ 8 \}}\) | \(0.00814 ^{\{ 2 \}}\) | \(0.0086 ^{\{ 6 \}}\) | \(0.00837 ^{\{ 5 \}}\) | \(0.0088 ^{\{ 7 \}}\) | \(0.00836 ^{\{ 4 \}}\) | |
\(\pmb K{_5}\) | \(0.01281 ^{\{ 1 \}}\) | \(0.0136 ^{\{ 3 \}}\) | \(0.01489 ^{\{ 8 \}}\) | \(0.01359 ^{\{ 2 \}}\) | \(0.01453 ^{\{ 6 \}}\) | \(0.01398 ^{\{ 5 \}}\) | \(0.01462 ^{\{ 7 \}}\) | \(0.01397 ^{\{ 4 \}}\) | |
\(\pmb K{_6}\) | \(0.00712 ^{\{ 1 \}}\) | \(0.00679 ^{\{ 3 \}}\) | \(0.00708 ^{\{ 8 \}}\) | \(0.00713 ^{\{ 2 \}}\) | \(0.00703 ^{\{ 6 \}}\) | \(0.00703 ^{\{ 5 \}}\) | \(0.00682 ^{\{ 7 \}}\) | \(0.00694 ^{\{ 4 \}}\) | |
\(\sum Ranks\) | \(21 ^{\{ 1 \}}\) | \(26.5 ^{\{ 2.5 \}}\) | \(68 ^{\{ 8 \}}\) | \(26.5 ^{\{ 2.5 \}}\) | \(54 ^{\{ 6 \}}\) | \(35 ^{\{ 4 \}}\) | \(58 ^{\{ 7 \}}\) | \(42 ^{\{ 5 \}}\) | |
500 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.03208 ^{\{ 1 \}}\) | \(0.03625 ^{\{ 4 \}}\) | \(0.04289 ^{\{ 10 \}}\) | \(0.03566 ^{\{ 2 \}}\) | \(0.04273 ^{\{ 9 \}}\) | \(0.04152 ^{\{ 6 \}}\) | \(0.04032 ^{\{ 5 \}}\) | \(0.03615 ^{\{ 3 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.0295 ^{\{ 1 \}}\) | \(0.03276 ^{\{ 8 \}}\) | \(0.03257 ^{\{ 7 \}}\) | \(0.03121 ^{\{ 4 \}}\) | \(0.03151 ^{\{ 5 \}}\) | \(0.03066 ^{\{ 2 \}}\) | \(0.03204 ^{\{ 6 \}}\) | \(0.03077 ^{\{ 3 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00163 ^{\{ 1 \}}\) | \(0.00212 ^{\{ 4 \}}\) | \(0.00281 ^{\{ 8 \}}\) | \(0.002 ^{\{ 2 \}}\) | \(0.00282 ^{\{ 9 \}}\) | \(0.00269 ^{\{ 6 \}}\) | \(0.00257 ^{\{ 5 \}}\) | \(0.00206 ^{\{ 3 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00134 ^{\{ 1 \}}\) | \(0.0017 ^{\{ 8 \}}\) | \(0.00169 ^{\{ 7 \}}\) | \(0.0016 ^{\{ 5 \}}\) | \(0.00156 ^{\{ 4 \}}\) | \(0.0015 ^{\{ 2.5 \}}\) | \(0.00162 ^{\{ 6 \}}\) | \(0.0015 ^{\{ 2.5 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.02138 ^{\{ 1 \}}\) | \(0.02417 ^{\{ 4 \}}\) | \(0.0286 ^{\{ 10 \}}\) | \(0.02377 ^{\{ 2 \}}\) | \(0.02849 ^{\{ 9 \}}\) | \(0.02768 ^{\{ 6 \}}\) | \(0.02688 ^{\{ 5 \}}\) | \(0.0241 ^{\{ 3 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.01475 ^{\{ 1 \}}\) | \(0.01638 ^{\{ 8 \}}\) | \(0.01629 ^{\{ 7 \}}\) | \(0.01561 ^{\{ 4 \}}\) | \(0.01576 ^{\{ 5 \}}\) | \(0.01533 ^{\{ 2 \}}\) | \(0.01602 ^{\{ 6 \}}\) | \(0.01539 ^{\{ 3 \}}\) | |
\(\pmb K{_4}\) | \(0.00677 ^{\{ 1 \}}\) | \(0.00752 ^{\{ 4 \}}\) | \(0.0079 ^{\{ 8 \}}\) | \(0.00733 ^{\{ 3 \}}\) | \(0.00776 ^{\{ 7 \}}\) | \(0.00766 ^{\{ 5 \}}\) | \(0.00772 ^{\{ 6 \}}\) | \(0.00721 ^{\{ 2 \}}\) | |
\(\pmb K{_5}\) | \(0.01121 ^{\{ 1 \}}\) | \(0.01254 ^{\{ 4 \}}\) | \(0.01336 ^{\{ 8 \}}\) | \(0.01219 ^{\{ 3 \}}\) | \(0.01311 ^{\{ 7 \}}\) | \(0.01279 ^{\{ 5 \}}\) | \(0.01286 ^{\{ 6 \}}\) | \(0.01208 ^{\{ 2 \}}\) | |
\(\pmb K{_6}\) | \(0.00626 ^{\{ 1 \}}\) | \(0.00609 ^{\{ 4 \}}\) | \(0.00614 ^{\{ 8 \}}\) | \(0.00624 ^{\{ 3 \}}\) | \(0.00625 ^{\{ 7 \}}\) | \(0.00616 ^{\{ 5 \}}\) | \(0.00596 ^{\{ 6 \}}\) | \(0.0061 ^{\{ 2 \}}\) | |
\(\sum Ranks\) | \(16 ^{\{ 1 \}}\) | \(46 ^{\{ 5.5 \}}\) | \(69 ^{\{ 8 \}}\) | \(31 ^{\{ 3 \}}\) | \(62 ^{\{ 7 \}}\) | \(39.5 ^{\{ 4 \}}\) | \(46 ^{\{ 5.5 \}}\) | \(24.5 ^{\{ 2 \}}\) |
n | Est. | LTADE | MSADE | MSALDE | ADSOE | KE | MSSD | MSSLD | MSLND |
|---|---|---|---|---|---|---|---|---|---|
30 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.18694 ^{\{ 11 \}}\) | \(0.20574^{\{ 13 \}}\) | \(0.18392 ^{\{ 10 \}}\) | \(0.27836 ^{\{ 16 \}}\) | \(0.19138 ^{\{ 12 \}}\) | \(0.24877 ^{\{ 15 \}}\) | \(0.1629 ^{\{ 4 \}}\) | \(0.24745 ^{\{ 14 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.13974 ^{\{ 9 \}}\) | \(0.19778 ^{\{ 15 \}}\) | \(0.1755 ^{\{ 12 \}}\) | \(0.2021 ^{\{ 16 \}}\) | \(0.14286 ^{\{ 10 \}}\) | \(0.18263 ^{\{ 13 \}}\) | \(0.16059 ^{\{ 11 \}}\) | \(0.18483 ^{\{ 14 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.05703 ^{\{ 11 \}}\) | \(0.06607 ^{\{ 13 \}}\) | \(0.05124 ^{\{ 9 \}}\) | \(0.12689 ^{\{ 16 \}}\) | \(0.06357 ^{\{ 12 \}}\) | \(0.09244 ^{\{ 15 \}}\) | \(0.04054 ^{\{ 3 \}}\) | \(0.09132 ^{\{ 14 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.03307 ^{\{ 9 \}}\) | \(0.06239 ^{\{ 15 \}}\) | \(0.0482 ^{\{ 12 \}}\) | \(0.08116 ^{\{ 16 \}}\) | \(0.03389 ^{\{ 10 \}}\) | \(0.05745 ^{\{ 13 \}}\) | \(0.0416 ^{\{ 11 \}}\) | \(0.06012 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.12462 ^{\{ 11 \}}\) | \(0.13716 ^{\{ 13 \}}\) | \(0.12262 ^{\{ 10 \}}\) | \(0.18557 ^{\{ 16 \}}\) | \(0.12759 ^{\{ 12 \}}\) | \(0.16585 ^{\{ 15 \}}\) | \(0.1086 ^{\{ 4 \}}\) | \(0.16496 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.06987 ^{\{ 9 \}}\) | \(0.09889 ^{\{ 15 \}}\) | \(0.08775 ^{\{ 12 \}}\) | \(0.10105 ^{\{ 16 \}}\) | \(0.07143 ^{\{ 10 \}}\) | \(0.09131 ^{\{ 13 \}}\) | \(0.0803 ^{\{ 11 \}}\) | \(0.09241 ^{\{ 14 \}}\) | |
\(\pmb K{_4}\) | \(0.03279 ^{\{ 9 \}}\) | \(0.0455 ^{\{ 13 \}}\) | \(0.04111 ^{\{ 12 \}}\) | \(0.04601 ^{\{ 14 \}}\) | \(0.03357 ^{\{ 10 \}}\) | \(0.04685 ^{\{ 15 \}}\) | \(0.0363 ^{\{ 11 \}}\) | \(0.04711 ^{\{ 16 \}}\) | |
\(\pmb K{_5}\) | \(0.05655 ^{\{ 9 \}}\) | \(0.07474 ^{\{ 13 \}}\) | \(0.06803 ^{\{ 12 \}}\) | \(0.08351 ^{\{ 16 \}}\) | \(0.05689 ^{\{ 10 \}}\) | \(0.07961 ^{\{ 14 \}}\) | \(0.05985 ^{\{ 11 \}}\) | \(0.08047 ^{\{ 15 \}}\) | |
\(\pmb K{_6}\) | \(0.06277 ^{\{ 9 \}}\) | \(0.09097 ^{\{ 13 \}}\) | \(0.05743 ^{\{ 12 \}}\) | \(0.12397 ^{\{ 16 \}}\) | \(0.08403 ^{\{ 10 \}}\) | \(0.11143 ^{\{ 14 \}}\) | \(0.04984 ^{\{ 11 \}}\) | \(0.10742 ^{\{ 15 \}}\) | |
\(\sum Ranks\) | \(87 ^{\{ 10 \}}\) | \(123 ^{\{ 13 \}}\) | \(97 ^{\{ 11 \}}\) | \(142 ^{\{ 16 \}}\) | \(98 ^{\{ 12 \}}\) | \(128 ^{\{ 14 \}}\) | \(69 ^{\{ 8 \}}\) | \(129 ^{\{ 15 \}}\) | |
80 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.11278 ^{\{ 11 \}}\) | \(0.1272 ^{\{ 13 \}}\) | \(0.11325 ^{\{ 12 \}}\) | \(0.17669 ^{\{ 16 \}}\) | \(0.1125 ^{\{ 10 \}}\) | \(0.14923 ^{\{ 15 \}}\) | \(0.10046 ^{\{ 5 \}}\) | \(0.1424 ^{\{ 14 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.08164 ^{\{ 7 \}}\) | \(0.12342 ^{\{ 14 \}}\) | \(0.10923 ^{\{ 12 \}}\) | \(0.12437 ^{\{ 15 \}}\) | \(0.08749 ^{\{ 10 \}}\) | \(0.13074 ^{\{ 16 \}}\) | \(0.10151 ^{\{ 11 \}}\) | \(0.11983 ^{\{ 13 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.02012 ^{\{ 11 \}}\) | \(0.0247 ^{\{ 13 \}}\) | \(0.01966 ^{\{ 10 \}}\) | \(0.05163 ^{\{ 16 \}}\) | \(0.02116 ^{\{ 12 \}}\) | \(0.03416 ^{\{ 15 \}}\) | \(0.0154 ^{\{ 6 \}}\) | \(0.03008 ^{\{ 14 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.01074 ^{\{ 9 \}}\) | \(0.02382 ^{\{ 14 \}}\) | \(0.01871 ^{\{ 12 \}}\) | \(0.02549 ^{\{ 15 \}}\) | \(0.01178 ^{\{ 10 \}}\) | \(0.02748 ^{\{ 16 \}}\) | \(0.01607 ^{\{ 11 \}}\) | \(0.02335 ^{\{ 13 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.07519 ^{\{ 11 \}}\) | \(0.0848 ^{\{ 13 \}}\) | \(0.0755 ^{\{ 12 \}}\) | \(0.11779 ^{\{ 16 \}}\) | \(0.075 ^{\{ 10 \}}\) | \(0.09948 ^{\{ 15 \}}\) | \(0.06697 ^{\{ 5 \}}\) | \(0.09494 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.04082 ^{\{ 7 \}}\) | \(0.06171 ^{\{ 14 \}}\) | \(0.05462 ^{\{ 12 \}}\) | \(0.06219 ^{\{ 15 \}}\) | \(0.04375 ^{\{ 10 \}}\) | \(0.06537 ^{\{ 16 \}}\) | \(0.05076 ^{\{ 11 \}}\) | \(0.05991 ^{\{ 13 \}}\) | |
\(\pmb K{_4}\) | \(0.01986 ^{\{ 9 \}}\) | \(0.02803 ^{\{ 13 \}}\) | \(0.02526 ^{\{ 12 \}}\) | \(0.02968 ^{\{ 15 \}}\) | \(0.02074 ^{\{ 10 \}}\) | \(0.03112 ^{\{ 16 \}}\) | \(0.02287 ^{\{ 11 \}}\) | \(0.02905 ^{\{ 14 \}}\) | |
\(\pmb K{_5}\) | \(0.0341 ^{\{ 9 \}}\) | \(0.04612 ^{\{ 13 \}}\) | \(0.04165 ^{\{ 12 \}}\) | \(0.0546 ^{\{ 16 \}}\) | \(0.03526 ^{\{ 10 \}}\) | \(0.05185 ^{\{ 15 \}}\) | \(0.0374 ^{\{ 11 \}}\) | \(0.04883 ^{\{ 14 \}}\) | |
\(\pmb K{_6}\) | \(0.02122 ^{\{ 9 \}}\) | \(0.02877 ^{\{ 13 \}}\) | \(0.02371 ^{\{ 12 \}}\) | \(0.04051 ^{\{ 16 \}}\) | \(0.02206 ^{\{ 10 \}}\) | \(0.03712 ^{\{ 15 \}}\) | \(0.02159 ^{\{ 11 \}}\) | \(0.03138 ^{\{ 14 \}}\) | |
\(\sum Ranks\) | \(83 ^{\{ 10 \}}\) | \(120 ^{\{ 13 \}}\) | \(106 ^{\{ 12 \}}\) | \(140 ^{\{ 16 \}}\) | \(93 ^{\{ 11 \}}\) | \(139 ^{\{ 15 \}}\) | \(81 ^{\{ 9 \}}\) | \(123 ^{\{ 14 \}}\) | |
150 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.08154 ^{\{ 11 \}}\) | \(0.08629 ^{\{ 13 \}}\) | \(0.08502 ^{\{ 12 \}}\) | \(0.13596 ^{\{ 16 \}}\) | \(0.07837 ^{\{ 9 \}}\) | \(0.1032 ^{\{ 15 \}}\) | \(0.07606 ^{\{ 7 \}}\) | \(0.10196 ^{\{ 14 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.05984 ^{\{ 8 \}}\) | \(0.09134 ^{\{ 13 \}}\) | \(0.08471 ^{\{ 12 \}}\) | \(0.09826 ^{\{ 15 \}}\) | \(0.06275 ^{\{ 10 \}}\) | \(0.10099 ^{\{ 16 \}}\) | \(0.07187 ^{\{ 11 \}}\) | \(0.0955 ^{\{ 14 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.01076 ^{\{ 11 \}}\) | \(0.01139 ^{\{ 13 \}}\) | \(0.01091 ^{\{ 12 \}}\) | \(0.02984 ^{\{ 16 \}}\) | \(0.01026 ^{\{ 10 \}}\) | \(0.01697 ^{\{ 15 \}}\) | \(0.00875 ^{\{ 6 \}}\) | \(0.01554 ^{\{ 14 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00575 ^{\{ 8 \}}\) | \(0.0131 ^{\{ 13 \}}\) | \(0.01131 ^{\{ 12 \}}\) | \(0.01517 ^{\{ 15 \}}\) | \(0.00628 ^{\{ 10 \}}\) | \(0.01603 ^{\{ 16 \}}\) | \(0.00811 ^{\{ 11 \}}\) | \(0.0144 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.05436 ^{\{ 11 \}}\) | \(0.05753 ^{\{ 13 \}}\) | \(0.05668 ^{\{ 12 \}}\) | \(0.09064 ^{\{ 16 \}}\) | \(0.05224 ^{\{ 9 \}}\) | \(0.0688 ^{\{ 15 \}}\) | \(0.0507 ^{\{ 7 \}}\) | \(0.06797 ^{\{ 14 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.02992 ^{\{ 8 \}}\) | \(0.04567 ^{\{ 13 \}}\) | \(0.04236 ^{\{ 12 \}}\) | \(0.04913 ^{\{ 15 \}}\) | \(0.03137 ^{\{ 10 \}}\) | \(0.0505 ^{\{ 16 \}}\) | \(0.03593 ^{\{ 11 \}}\) | \(0.04775 ^{\{ 14 \}}\) | |
\(\pmb K{_4}\) | \(0.01471 ^{\{ 8.5 \}}\) | \(0.02023 ^{\{ 13 \}}\) | \(0.01912 ^{\{ 12 \}}\) | \(0.02308 ^{\{ 15 \}}\) | \(0.01482 ^{\{ 10 \}}\) | \(0.02315 ^{\{ 16 \}}\) | \(0.01635 ^{\{ 11 \}}\) | \(0.02214 ^{\{ 14 \}}\) | |
\(\pmb K{_5}\) | \(0.02518 ^{\{ 9 \}}\) | \(0.03317 ^{\{ 13 \}}\) | \(0.0313 ^{\{ 12 \}}\) | \(0.04294 ^{\{ 16 \}}\) | \(0.02519 ^{\{ 10 \}}\) | \(0.0383 ^{\{ 15 \}}\) | \(0.02705 ^{\{ 11 \}}\) | \(0.03664 ^{\{ 14 \}}\) | |
\(\pmb K{_6}\) | \(0.01391 ^{\{ 9 \}}\) | \(0.01798 ^{\{ 13 \}}\) | \(0.01638 ^{\{ 12 \}}\) | \(0.02545 ^{\{ 16 \}}\) | \(0.01383 ^{\{ 10 \}}\) | \(0.0208 ^{\{ 15 \}}\) | \(0.01533 ^{\{ 11 \}}\) | \(0.01928 ^{\{ 14 \}}\) | |
\(\sum Ranks\) | \(84.5 ^{\{ 9 \}}\) | \(117 ^{\{ 13 \}}\) | \(108 ^{\{ 12 \}}\) | \(140 ^{\{ 16 \}}\) | \(87 ^{\{ 11 \}}\) | \(139 ^{\{ 15 \}}\) | \(86 ^{\{ 10 \}}\) | \(126 ^{\{ 14 \}}\) | |
300 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.05593 ^{\{ 10 \}}\) | \(0.06365 ^{\{ 13 \}}\) | \(0.05674 ^{\{ 12 \}}\) | \(0.10639 ^{\{ 16 \}}\) | \(0.05657 ^{\{ 11 \}}\) | \(0.07046 ^{\{ 14 \}}\) | \(0.05381 ^{\{ 7 \}}\) | \(0.07253 ^{\{ 15 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.04229 ^{\{ 8 \}}\) | \(0.06383 ^{\{ 13 \}}\) | \(0.05808 ^{\{ 12 \}}\) | \(0.07576 ^{\{ 15 \}}\) | \(0.0464 ^{\{ 10 \}}\) | \(0.07072 ^{\{ 14 \}}\) | \(0.05608 ^{\{ 11 \}}\) | \(0.07614 ^{\{ 16 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00507 ^{\{ 11 \}}\) | \(0.00612 ^{\{ 13 \}}\) | \(0.00505 ^{\{ 10 \}}\) | \(0.01911 ^{\{ 16 \}}\) | \(0.00516 ^{\{ 12 \}}\) | \(0.00764 ^{\{ 14 \}}\) | \(0.00456 ^{\{ 8 \}}\) | \(0.00779 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00275 ^{\{ 8 \}}\) | \(0.00639 ^{\{ 13 \}}\) | \(0.00526 ^{\{ 12 \}}\) | \(0.00913 ^{\{ 15 \}}\) | \(0.00334 ^{\{ 10 \}}\) | \(0.00803 ^{\{ 14 \}}\) | \(0.00488 ^{\{ 11 \}}\) | \(0.00915 ^{\{ 16 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.03729 ^{\{ 10 \}}\) | \(0.04243 ^{\{ 13 \}}\) | \(0.03783 ^{\{ 12 \}}\) | \(0.07093 ^{\{ 16 \}}\) | \(0.03771 ^{\{ 11 \}}\) | \(0.04697 ^{\{ 14 \}}\) | \(0.03587 ^{\{ 7 \}}\) | \(0.04836 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.02114 ^{\{ 8 \}}\) | \(0.03192 ^{\{ 13 \}}\) | \(0.02904 ^{\{ 12 \}}\) | \(0.03788 ^{\{ 15 \}}\) | \(0.0232 ^{\{ 10 \}}\) | \(0.03536 ^{\{ 14 \}}\) | \(0.02804 ^{\{ 11 \}}\) | \(0.03807 ^{\{ 16 \}}\) | |
\(\pmb K{_4}\) | \(0.01028 ^{\{ 8 \}}\) | \(0.01422 ^{\{ 13 \}}\) | \(0.01298 ^{\{ 12 \}}\) | \(0.01776 ^{\{ 16 \}}\) | \(0.0109 ^{\{ 10 \}}\) | \(0.01593 ^{\{ 14 \}}\) | \(0.01234 ^{\{ 11 \}}\) | \(0.0169 ^{\{ 15 \}}\) | |
\(\pmb K{_5}\) | \(0.01751 ^{\{ 8 \}}\) | \(0.02345 ^{\{ 13 \}}\) | \(0.02125 ^{\{ 12 \}}\) | \(0.03355 ^{\{ 16 \}}\) | \(0.01849 ^{\{ 10 \}}\) | \(0.02614 ^{\{ 14 \}}\) | \(0.02033 ^{\{ 11 \}}\) | \(0.02778 ^{\{ 15 \}}\) | |
\(\pmb K{_6}\) | \(0.0092 ^{\{ 8 \}}\) | \(0.01182 ^{\{ 13 \}}\) | \(0.01104 ^{\{ 12 \}}\) | \(0.01814 ^{\{ 16 \}}\) | \(0.0091 ^{\{ 10 \}}\) | \(0.01314 ^{\{ 14 \}}\) | \(0.01024 ^{\{ 11 \}}\) | \(0.01332 ^{\{ 15 \}}\) | |
\(\sum Ranks\) | \(81 ^{\{ 9 \}}\) | \(117 ^{\{ 13 \}}\) | \(106 ^{\{ 12 \}}\) | \(141 ^{\{ 16 \}}\) | \(93 ^{\{ 11 \}}\) | \(126 ^{\{ 14 \}}\) | \(88 ^{\{ 10 \}}\) | \(138 ^{\{ 15 \}}\) |
400 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.04877 ^{\{ 11 \}}\) | \(0.0548 ^{\{ 13 \}}\) | \(0.05157 ^{\{ 12 \}}\) | \(0.08702 ^{\{ 16 \}}\) | \(0.04854 ^{\{ 10 \}}\) | \(0.06076 ^{\{ 14 \}}\) | \(0.04743 ^{\{ 9 \}}\) | \(0.06321 ^{\{ 15 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.03671 ^{\{ 7 \}}\) | \(0.05668 ^{\{ 13 \}}\) | \(0.04949 ^{\{ 12 \}}\) | \(0.06304 ^{\{ 14 \}}\) | \(0.03786 ^{\{ 10 \}}\) | \(0.06572 ^{\{ 16 \}}\) | \(0.04555 ^{\{ 11 \}}\) | \(0.06333 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00383 ^{\{ 11 \}}\) | \(0.00467 ^{\{ 13 \}}\) | \(0.00395 ^{\{ 12 \}}\) | \(0.01263 ^{\{ 16 \}}\) | \(0.00377 ^{\{ 10 \}}\) | \(0.00579 ^{\{ 14 \}}\) | \(0.00358 ^{\{ 9 \}}\) | \(0.0062 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00209 ^{\{ 6 \}}\) | \(0.00509 ^{\{ 13 \}}\) | \(0.0039 ^{\{ 12 \}}\) | \(0.00641 ^{\{ 14 \}}\) | \(0.00229 ^{\{ 10 \}}\) | \(0.00671 ^{\{ 16 \}}\) | \(0.00331 ^{\{ 11 \}}\) | \(0.00642 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.03252 ^{\{ 11 \}}\) | \(0.03654 ^{\{ 13 \}}\) | \(0.03438 ^{\{ 12 \}}\) | \(0.05801 ^{\{ 16 \}}\) | \(0.03236 ^{\{ 10 \}}\) | \(0.0405 ^{\{ 14 \}}\) | \(0.03162 ^{\{ 9 \}}\) | \(0.04214 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.01835 ^{\{ 7 \}}\) | \(0.02834 ^{\{ 13 \}}\) | \(0.02475 ^{\{ 12 \}}\) | \(0.03152 ^{\{ 14 \}}\) | \(0.01893 ^{\{ 10 \}}\) | \(0.03286 ^{\{ 16 \}}\) | \(0.02278 ^{\{ 11 \}}\) | \(0.03167 ^{\{ 15 \}}\) | |
\(\pmb K{_4}\) | \(0.00889 ^{\{ 9 \}}\) | \(0.0126 ^{\{ 13 \}}\) | \(0.01123 ^{\{ 12 \}}\) | \(0.01465 ^{\{ 16 \}}\) | \(0.0092 ^{\{ 10 \}}\) | \(0.0145 ^{\{ 15 \}}\) | \(0.01042 ^{\{ 11 \}}\) | \(0.01417 ^{\{ 14 \}}\) | |
\(\pmb K{_5}\) | \(0.01527 ^{\{ 9 \}}\) | \(0.02062 ^{\{ 13 \}}\) | \(0.01849 ^{\{ 12 \}}\) | \(0.02736 ^{\{ 16 \}}\) | \(0.0155 ^{\{ 10 \}}\) | \(0.02377 ^{\{ 15 \}}\) | \(0.01705 ^{\{ 11 \}}\) | \(0.02334 ^{\{ 14 \}}\) | |
\(\pmb K{_6}\) | \(0.0077 ^{\{ 9 \}}\) | \(0.01015 ^{\{ 13 \}}\) | \(0.00911 ^{\{ 12 \}}\) | \(0.01418 ^{\{ 16 \}}\) | \(0.00778 ^{\{ 10 \}}\) | \(0.01127 ^{\{ 15 \}}\) | \(0.00866 ^{\{ 11 \}}\) | \(0.01115 ^{\{ 14 \}}\) | |
\(\sum Ranks\) | \(80 ^{\{ 9 \}}\) | \(117 ^{\{ 13 \}}\) | \(108 ^{\{ 12 \}}\) | \(138 ^{\{ 16 \}}\) | \(90 ^{\{ 10 \}}\) | \(135 ^{\{ 15 \}}\) | \(93 ^{\{ 11 \}}\) | \(132 ^{\{ 14 \}}\) | |
500 | \(\pmb K{_1}\)(\(\hat{\alpha }\)) | \(0.04335 ^{\{ 11 \}}\) | \(0.04963 ^{\{ 13 \}}\) | \(0.04255 ^{\{ 8 \}}\) | \(0.08403 ^{\{ 16 \}}\) | \(0.04391 ^{\{ 12 \}}\) | \(0.05382 ^{\{ 14 \}}\) | \(0.04172 ^{\{ 7 \}}\) | \(0.0552 ^{\{ 15 \}}\) |
\(\pmb K{_1}\)(\(\hat{\beta }\)) | \(0.03352 ^{\{ 9 \}}\) | \(0.05132 ^{\{ 13 \}}\) | \(0.04464 ^{\{ 12 \}}\) | \(0.06191 ^{\{ 16 \}}\) | \(0.03384 ^{\{ 10 \}}\) | \(0.05794 ^{\{ 14 \}}\) | \(0.04333 ^{\{ 11 \}}\) | \(0.05924 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\alpha }\)) | \(0.00308 ^{\{ 12 \}}\) | \(0.00381 ^{\{ 13 \}}\) | \(0.00287 ^{\{ 10 \}}\) | \(0.01146 ^{\{ 16 \}}\) | \(0.00293 ^{\{ 11 \}}\) | \(0.00456 ^{\{ 14 \}}\) | \(0.00272 ^{\{ 7 \}}\) | \(0.00476 ^{\{ 15 \}}\) | |
\(\pmb K{_2}\)(\(\hat{\beta }\)) | \(0.00175 ^{\{ 9 \}}\) | \(0.00429 ^{\{ 13 \}}\) | \(0.00316 ^{\{ 12 \}}\) | \(0.00593 ^{\{ 16 \}}\) | \(0.00177 ^{\{ 10 \}}\) | \(0.00533 ^{\{ 14 \}}\) | \(0.00299 ^{\{ 11 \}}\) | \(0.00545 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\alpha }\)) | \(0.0289 ^{\{ 11 \}}\) | \(0.03309 ^{\{ 13 \}}\) | \(0.02837 ^{\{ 8 \}}\) | \(0.05602 ^{\{ 16 \}}\) | \(0.02927 ^{\{ 12 \}}\) | \(0.03588 ^{\{ 14 \}}\) | \(0.02782 ^{\{ 7 \}}\) | \(0.0368 ^{\{ 15 \}}\) | |
\(\pmb K{_3}\)(\(\hat{\beta }\)) | \(0.01676 ^{\{ 9 \}}\) | \(0.02566 ^{\{ 13 \}}\) | \(0.02232 ^{\{ 12 \}}\) | \(0.03096 ^{\{ 16 \}}\) | \(0.01692 ^{\{ 10 \}}\) | \(0.02897 ^{\{ 14 \}}\) | \(0.02167 ^{\{ 11 \}}\) | \(0.02962 ^{\{ 15 \}}\) | |
\(\pmb K{_4}\) | \(0.00804 ^{\{ 9 \}}\) | \(0.01146 ^{\{ 13 \}}\) | \(0.00989 ^{\{ 12 \}}\) | \(0.01409 ^{\{ 16 \}}\) | \(0.00815 ^{\{ 10 \}}\) | \(0.01276 ^{\{ 14 \}}\) | \(0.00964 ^{\{ 11 \}}\) | \(0.01299 ^{\{ 15 \}}\) | |
\(\pmb K{_5}\) | \(0.01378 ^{\{ 9 \}}\) | \(0.01871 ^{\{ 13 \}}\) | \(0.01615 ^{\{ 12 \}}\) | \(0.02673 ^{\{ 16 \}}\) | \(0.01382 ^{\{ 10 \}}\) | \(0.02088 ^{\{ 14 \}}\) | \(0.01576 ^{\{ 11 \}}\) | \(0.02129 ^{\{ 15 \}}\) | |
\(\pmb K{_6}\) | \(0.00683 ^{\{ 9 \}}\) | \(0.00888 ^{\{ 13 \}}\) | \(0.00814 ^{\{ 12 \}}\) | \(0.01343 ^{\{ 16 \}}\) | \(0.00675 ^{\{ 10 \}}\) | \(0.00983 ^{\{ 14 \}}\) | \(0.00761 ^{\{ 11 \}}\) | \(0.00979 ^{\{ 15 \}}\) | |
\(\sum Ranks\) | \(89 ^{\{ 10 \}}\) | \(117 ^{\{ 13 \}}\) | \(98 ^{\{ 12 \}}\) | \(144 ^{\{ 16 \}}\) | \(94 ^{\{ 11 \}}\) | \(127 ^{\{ 14 \}}\) | \(87 ^{\{ 9 \}}\) | \(134 ^{\{ 15 \}}\) |
