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Table 2 MLE estimates for the parameters of \(\mathcal {EGW}\) distribution with simulated data from \(\mathcal {EGW}\) 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 a b \(\alpha\) \(\beta\)
50 BFGS Estimates 6.559792 4.508665 3.222132 5.679618
SE 21.726748 5.959038 142.025577 2.451735
MSE 21.252218 30.410082 0.624046 5.544654
SANN Estimates 5.758308 4.205869 3.638858 5.638019
SE 5.773811 5.391740 1.419861 2.597639
MSE 36.580530 17.459904 0.942536 4.807788
Nelder–Mead Estimates 2.445578 4.636861 4.541140 5.677241
SE 34.326846 6.496251 71.788950 2.461764
MSE 10.188337 39.203020 2.132110 5.576713
Time 0d:16h:57m:32s (61052 s)
100 BFGS Estimates 10.076350 3.687458 2.938870 5.431711
SE 3.324494 2.853083 7.095580 1.568548
MSE 66.070093 9.705820 1.132114 2.587435
SANN Estimates 5.860451 3.682335 3.611025 5.428296
SE 5.255925 2.956691 1.248130 1.629309
MSE 38.041064 9.051131 0.890948 2.579751
Nelder–Mead Estimates 1.833553 3.704633 4.466173 5.430765
SE 29.335765 2.898004 27.704366 1.570119
MSE 3.074604 10.360465 1.047837 2.595298
Time 1d:21h:45m:2s (164702 s)
500 BFGS Estimates 10.228551 3.052343 2.898200