Moments

$\mu$

${\sigma }^2$

${\beta }_1$

${\beta }_2$

$x_0$

CV

$\alpha$

$\beta =5$ and $\theta =2$

1

0.4286

0.0544

10.834

40.6406

0.2953

54.4331

1.5

0.5542

0.0339

3.4111

10.9975

0.4591

33.2280

2

0.6364

0.0235

1.9645

7.2988

0.5653

24.0887

2.5

0.6937

0.0172

1.3898

5.9656

0.6379

18.9322

3

0.7355

0.0132

1.0898

5.2979

0.6901

15.6069

$\beta$

$\alpha =5$ and $\theta =4$

1

1.4748

0.2105

12.8181

49.0615

1.2219

31.1092

1.5

1.2877

0.0751

4.3933

13.5845

1.1444

21.2754

2

1.1880

0.0406

2.5336

8.6368

1.0905

16.9685

2.5

1.1224

0.0264

1.7504

6.7687

1.0496

14.4740

3

1.0745

0.0190

1.3258

5.8052

1.0169

12.8146

$\theta$

$\alpha =2$ and $\beta =3$

1

0.5816

0.0368

5.2168

17.4302

0.4816

32.9653

1.5

0.7236

0.0597

5.4722

18.0293

0.5949

33.7764

2

0.8460

0.0843

5.5922

18.2726

0.6920

34.3214

2.5

0.9554

0.1099

5.6520

18.3749

0.7787

34.7060

3

1.0553

0.1363

5.6824

18.4154

0.8579

34.9879