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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