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Table 3 MLE estimates for the parameters of \(\mathcal {EW}\) distribution with simulated data from \(\mathcal {EW}\) distribution via BFGS, SANN, and Nelder–Mead algorithms

From: Analyzing and solving the identifiability problem in the exponentiated generalized Weibull distribution

n Method Inference results b c \(\beta\)
50 BFGS Estimates 4.402925 4.102611 5.949618
SE 5.697425 0.751590 2.601159
MSE 22.795855 0.402740 9.699106
SANN Estimates 4.449711 4.106828 5.920183
SE 6.085270 0.789521 2.686872
MSE 24.098193 0.413645 8.739624
Nelder–Mead Estimates 4.472318 4.107355 5.951902
SE 5.962889 0.764355 2.603384
MSE 25.399142 0.420800 10.046063
Time 0d:8h:50m:45s (31845 s)
100 BFGS Estimates 4.213534 4.113357 5.299846
SE 3.566710 0.509471 1.548855
MSE 18.221747 0.290249 2.756462
SANN Estimates 4.207505 4.114013 5.297310
SE 3.650426 0.521174 1.571037
MSE 17.379728 0.288609 2.753479
Nelder–Mead Estimates 4.249701 4.115646 5.298766
SE 3.666593 0.513693 1.549940
MSE 19.982132 0.299304 2.763964
Time 0d:15h:18m:26s (55106 s)
500 BFGS Estimates 3.155945 4.017774 5.055031
SE 0.906044 0.185317 0.627086
MSE 0.906766 0.035019 0.396619
SANN Estimates 3.157440 4.017996 5.054715
SE 0.911430 0.186253 0.629546
MSE 0.911503 0.035196 0.398176
Nelder–Mead Estimates 3.156035 4.017759 5.055316
SE 0.906550 0.185396 0.627336
MSE 0.908748 0.035088 0.397327
Time 2d:16h:15m:17s (231317 s)
1000 BFGS Estimates 3.078456 4.009790 5.023386
SE 0.609515 0.128449 0.437921
MSE 0.390373 0.016572 0.189574
SANN Estimates 3.078632 4.009775 5.023852
SE 0.611345 0.128798 0.439047
MSE 0.393664 0.016703 0.190998
Nelder–Mead Estimates 3.077648 4.009598 5.024238
SE 0.609420 0.128441 0.438062
MSE 0.391118 0.016610 0.190232
Time 4d:12h:27m:34s (390454 s)