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Table 2 Bias and SD of the parameter estimates using MLE method

From: Generalized logistic distribution and its regression model

Parameters Sample size Bias SD
ξ μ σ \( \hat{\xi}-\xi \) \( \hat{\mu}-\mu \) \( \hat{\sigma}-\sigma \) \( SD\left(\hat{\xi}\right) \) \( SD\left(\hat{\mu}\right) \) \( SD\left(\hat{\sigma}\right) \)
0.5 −1 − 1 50 0.2585 −0.1125 −0.0425 0.5947 0.3552 0.2162
100 0.0979 −0.0386 − 0.0160 0.3570 0.2413 0.1550
200 0.0654 −0.0278 −0.0142 0.2278 0.1587 0.1187
500 0.0265 −0.0070 − 0.0050 0.1357 0.0999 0.0687
1000 0.0102 0.0003 −0.0010 0.0928 0.0662 0.0474
2 0 −2 50 1.0074 −0.4525 −0.1085 2.5277 1.3595 0.6366
100 0.3699 −0.1655 − 0.0345 1.4639 0.8721 0.4376
200 0.3072 −0.1583 −0.0494 1.1224 0.6916 0.3598
500 0.1615 −0.0767 − 0.0279 0.8690 0.5048 0.2375
1000 0.0439 −0.0156 −0.0061 0.4078 0.2709 0.1442
6 2 −3 50 −1.3031 0.9211 0.4806 2.9698 1.5575 0.7229
100 −0.8896 0.6087 0.2896 2.6342 1.3797 0.6079
200 −0.4115 0.3154 0.1566 2.2743 1.1780 0.5040
500 −0.4251 0.2871 0.1219 1.8211 0.9216 0.3595
1000 −0.4952 0.2921 0.1137 1.3108 0.6636 0.2506
0.5 −1 1 50 0.2017 0.0813 0.0291 0.5106 0.3185 0.2133
100 0.0981 0.0387 0.0161 0.3569 0.2412 0.1550
200 0.0659 0.0283 0.0141 0.2289 0.1591 0.1189
500 0.0271 0.0074 0.0054 0.1364 0.1004 0.0688
1000 0.0116 0.0004 0.0018 0.0920 0.0662 0.0475
2 0 2 50 0.9262 0.4091 0.0931 2.3871 1.2927 0.6084
100 0.3652 0.1627 0.0334 1.4761 0.8769 0.4393
200 0.3072 0.1585 0.0513 1.1224 0.6939 0.3609
500 0.1562 0.0713 0.0251 0.9162 0.5125 0.2358
1000 0.0365 0.0106 0.0034 0.4089 0.2720 0.1444
6 4 3 50 1.0664 0.0219 −0.1725 6.0035 2.5586 0.9517
100 0.8875 0.1094 −0.0699 5.0824 2.2413 0.8278
200 0.6818 0.1183 −0.0310 3.9748 1.7626 0.6446
500 0.4806 0.0767 −0.0105 3.7760 1.6030 0.5314
1000 0.1190 −0.0384 − 0.0374 2.7782 1.2040 0.3957