Table 2 Simulated biases and MSEs for different estimation procedures for parameter setting α=1.0,ν=0.5

n=20

β=1.0

Method 1

0.0195

0.0425

0.9742

4.0217

0.2869

0.3524

Method 2

0.0434

0.0813

0.4214

2.2961

0.0974

0.2553

Method 3

0.0195

0.0425

0.1487

2.1084

–0.0322

0.2548

Method 4

0.0434

0.0813

–0.4201

1.3537

–0.2534

0.2354

Method 5

0.0307

0.0529

1.3228

7.3012

0.3447

0.4640

β=1.5

Method 1

0.0381

0.0932

0.9322

3.2543

0.2855

0.3089

Method 2

0.0650

0.1731

0.3446

1.7079

0.0759

0.2060

Method 3

0.0381

0.0932

0.0979

1.6965

–0.0443

0.2157

Method 4

0.0650

0.1731

–0.4908

1.1100

–0.2836

0.2131

Method 5

0.0408

0.1285

1.4301

7.0455

0.3891

0.4982

β=0.5

Method 1

0.0108

0.0102

0.9442

4.3086

0.2758

0.3304

Method 2

0.0217

0.0216

0.4038

2.0323

0.0936

0.2282

Method 3

0.0108

0.0102

0.1228

2.1729

–0.0445

0.2402

Method 4

0.0217

0.0216

–0.4360

1.2374

–0.2616

0.2193

Method 7

0.0095

0.0125

1.4200

7.2533

0.3673

0.4795

n=40

β=1.0

Method 1

0.0174

0.0208

0.4064

1.1396

0.1259

0.1394

Method 2

0.0267

0.0434

0.1390

0.8548

0.0183

0.1206

Method 3

0.0174

0.0208

–0.0899

0.9007

–0.0928

0.1441

Method 4

0.0267

0.0434

–0.4459

0.8461

–0.2485

0.1733

Method 5

0.0112

0.0220

0.5577

1.6258

0.1622

0.1789

β=1.5

Method 1

0.0130

0.0433

0.3903

1.1135

0.1147

0.1417

Method 2

0.0244

0.0859

0.1178

0.7991

0.0066

0.1238

Method 3

0.0130

0.0433

–0.0822

0.8952

–0.0911

0.1470

Method 4

0.0244

0.0859

–0.4382

0.7508

–0.2415

0.1621

Method 5

0.0140

0.0495

0.5002

1.5122

0.1441

0.1717

β=0.5

Method 1

0.0037

0.0050

0.3697

1.0955

0.1061

0.1347

Method 2

0.0060

0.0093

0.1313

0.8476

0.0104

0.1214

Method 3

0.0037

0.0050

–0.1212

0.8887

–0.1097

0.1481

Method 4

0.0060

0.0093

–0.4268

0.8502

–0.2423

0.1716

Method 5

–0.0001

0.0056

0.5676

1.5449

0.1693

0.1721

n=60

β=1.0

Method 1

–0.0023

0.0120

0.2280

0.6084

0.0645

0.0888

Method 2

0.0046

0.0267

0.0521

0.5265

–0.0104

0.0873

Method 3

–0.0023

0.0120

–0.1512

0.5816

–0.1065

0.1105

Method 4

0.0046

0.0267

–0.4006

0.6432

–0.2208

0.1402

Method 5

0.0132

0.0138

0.3006

0.7754

0.0893

0.1049

β=1.5

Method 1

0.0089

0.0309

0.2217

0.6390

0.0642

0.0901

Method 2

0.0178

0.0562

0.0497

0.5494

–0.0094

0.0881

Method 3

0.0089

0.0309

–0.1560

0.6107

–0.1074

0.1129

Method 4

0.0178

0.0562

–0.3966

0.6474

–0.2171

0.1368

Method 5

0.0044

0.0330

0.3469

0.8634

0.1039

0.1131

β=0.5

Method 1

0.0018

0.0032

0.2649

0.6466

0.0822

0.0934

Method 2

0.0026

0.1010

0.0850

0.5690

0.0053

0.0911

Method 3

0.0018

0.0032

–0.1172

0.5847

–0.0889

0.0145

Method 4

0.0026

0.1010

–0.3739

0.6695

–0.2078

0.1414

Method 5

0.0009

0.0033

0.3197

0.7679

0.0986

0.1013