Table 3 Simulated biases and MSEs for different estimation procedures for parameter setting α=2.0,ν=0.5

n=20

β=1.0

Method 1

0.0386

0.1125

1.3195

7.9982

0.1482

0.0990

Method 2

0.1371

0.4192

0.0557

2.9805

–0.0424

0.0740

Method 3

0.0386

0.1125

0.4002

4.6121

–0.0118

0.0910

Method 4

0.1371

0.4192

–1.1470

3.0691

–0.3047

0.1604

Method 5

0.0749

0.1563

1.6102

12.0105

0.1629

0.1341

β=1.5

Method 1

0.0741

0.2669

1.2255

6.2592

0.1490

0.0933

Method 2

0.2483

0.9636

0.0169

2.5749

–0.0439

0.0760

Method 3

0.0741

0.2669

0.3387

3.8775

–0.0086

0.0843

Method 4

0.2483

0.9636

–1.1137

3.0016

–0.2946

0.1566

Method 5

0.0736

0.2879

1.8437

14.1580

0.1863

0.1367

β=0.5

Method 1

0.0300

0.0311

1.1648

6.3143

0.1345

0.0929

Method 2

0.0830

0.1013

0.0232

2.9223

–0.0484

0.0799

Method 3

0.0300

0.0311

0.2871

3.8638

–0.0234

0.0886

Method 4

0.0830

0.1013

–1.0694

3.2768

–0.2920

0.1621

Method 5

0.0712

0.2610

1.7594

12.6750

0.1843

0.1315

n=40

β=1.0

Method 1

0.0283

0.0510

0.4013

1.8797

0.0427

0.0391

Method 2

0.0675

0.1607

–0.1425

1.3239

–0.0564

0.0424

Method 3

0.0283

0.0510

–0.0800

1.4982

–0.0522

0.0469

Method 4

0.0675

0.1607

–0.9059

2.0129

–0.2316

0.1069

Method 5

0.0253

0.0554

0.6419

2.4061

0.0782

0.0458

β=1.5

Method 1

0.0386

0.1025

0.5161

1.9371

0.0593

0.0384

Method 2

0.1448

0.4378

–0.0506

1.2901

–0.0414

0.0429

Method 3

0.0386

0.1025

0.0286

1.5041

–0.0350

0.0453

Method 4

0.1448

0.4378

–0.8061

1.8517

–0.2089

0.0993

Method 5

0.0369

0.1242

0.6034

2.3951

0.0697

0.0439

β=0.5

Method 1

0.0111

0.0126

0.5099

2.0122

0.0580

0.0370

Method 2

0.0450

0.0478

–0.0599

1.4283

–0.0459

0.0443

Method 3

0.0111

0.0126

0.0191

1.5585

–0.0372

0.0440

Method 4

0.0450

0.0478

–0.8308

2.0662

–0.2190

0.1056

Method 5

0.0121

0.0142

0.7498

2.9983

0.0894

0.0511

n=60

β=1.0

Method 1

0.0101

0.0312

0.3484

1.2761

0.0380

0.0300

Method 2

0.0454

0.1185

–0.0580

0.9684

–0.0351

0.0315

Method 3

0.0101

0.0312

0.0024

1.0757

–0.0282

0.0327

Method 4

0.0454

0.1185

–0.6773

1.4934

–0.1730

0.0763

Method 5

0.0117

0.0341

0.4055

1.3271

0.0490

0.0275

β=1.5

Method 1

0.0288

0.0703

0.2911

0.9903

0.0348

0.0239

Method 2

0.0813

0.2419

–0.0925

0.7792

–0.0361

0.0269

Method 3

0.0288

0.0703

–0.0473

0.8886

–0.0320

0.0278

Method 4

0.0813

0.2419

–0.6837

1.3505

–0.1694

0.0701

Method 5

0.0366

0.0835

0.3219

1.1432

0.0369

0.0272

β=0.5

Method 1

0.0120

0.0091

0.3565

1.1113

0.0423

0.0255

Method 2

0.0365

0.0323

–0.0721

0.8640

–0.0365

0.0296

Method 3

0.0120

0.0091

0.0150

0.9128

–0.0228

0.0269

Method 4

0.0365

0.0323

–0.6760

1.3800

–0.1699

0.0720

Method 5

0.0051

0.0081

0.3621

1.2234

0.0432

0.0260