Table 4 Simulated biases and MSEs for different estimation procedures for parameter setting α=1.0,ν=0.9

n=20

β=1.0

Method 1

0.0098

0.0132

0.8859

4.1859

0.4528

1.0031

Method 2

0.0126

0.0243

0.4174

2.6917

0.1578

0.7571

Method 3

0.0098

0.0132

0.0205

2.1971

–0.1634

0.7715

Method 4

0.0126

0.0243

–0.4101

1.4524

–0.4618

0.7328

Method 5

0.0083

0.0153

1.4731

7.7400

0.6839

1.6105

β=1.5

Method 1

0.0130

0.0309

0.8992

3.9446

0.4732

1.0613

Method 2

0.0220

0.0545

0.4182

2.1596

0.1773

0.7605

Method 3

0.0130

0.0309

0.0643

2.2646

–0.1191

0.7975

Method 4

0.0220

0.0545

–0.4120

1.3491

–0.4478

0.7151

Method 5

0.0174

0.0324

1.3639

6.1369

0.6680

1.4928

β=0.5

Method 1

0.0016

0.0033

0.8285

3.4397

0.4223

0.9522

Method 2

0.0022

0.0060

0.3769

1.9818

0.1481

0.6989

Method 3

0.0016

0.0033

–0.0263

1.8751

–0.1866

0.7413

Method 4

0.0022

0.0060

–0.4537

1.2252

–0.4826

0.6884

Method 5

0.0041

0.0039

1.3170

6.0487

0.6453

1.4899

n=40

β=1.0

Method 1

0.0038

0.0066

0.3101

0.9566

0.1507

0.4135

Method 2

0.0058

0.0128

0.1039

0.7441

0.0009

0.3774

Method 3

0.0038

0.0066

–0.1887

0.7752

–0.2426

0.4574

Method 4

0.0058

0.0128

–0.4548

0.7507

–0.4519

0.5265

Method 5

0.0029

0.0070

0.5476

1.5316

0.2904

0.5658

β=1.5

Method 1

0.0002

0.0144

0.3060

1.0136

0.1518

0.4263

Method 2

0.0002

0.0270

0.1067

0.8040

0.0045

0.3930

Method 3

0.0002

0.0144

–0.2057

0.8406

–0.2554

0.4841

Method 4

0.0002

0.0270

–0.4648

0.8255

–0.4624

0.5604

Method 5

0.0102

0.0149

0.5592

1.5119

0.3069

0.5646

β=0.5

Method 1

–0.0010

0.0015

0.3810

1.0063

0.2074

0.4302

Method 2

–0.0004

0.0029

0.1759

0.7747

0.0596

0.3760

Method 3

–0.0010

0.0015

–0.1378

0.7647

–0.1964

0.4470

Method 4

–0.0004

0.0029

–0.4162

0.7652

–0.4181

0.5223

Method 5

0.0015

0.0017

0.5205

1.5198

0.2768

0.5461

n=60

β=1.0

Method 1

0.0012

0.0042

0.1727

0.5760

0.0825

0.2853

Method 2

0.0017

0.0076

0.0400

0.5214

–0.0212

0.2874

Method 3

0.0012

0.0042

–0.2268

0.5858

–0.2465

0.3796

Method 4

0.0017

0.0076

–0.4125

0.6330

–0.4002

0.4547

Method 5

0.0013

0.0041

0.3112

0.7285

0.1738

0.3287

β=1.5

Method 1

–0.0019

0.0094

0.2492

0.6194

0.1329

0.2882

Method 2

–0.1581

0.0429

0.1031

0.5236

0.0221

0.2745

Method 3

–0.0019

0.0094

–0.0013

0.5552

–0.0017

0.3187

Method 4

–0.1581

0.0429

–0.3658

0.5916

–0.3655

0.4219

Method 5

0.0072

0.0104

0.3172

0.7224

0.1742

0.3264

β=0.5

Method 1

0.0017

0.0010

0.1963

0.5976

0.0976

0.2855

Method 2

0.0032

0.0020

0.0502

0.5026

–0.0130

0.2738

Method 3

0.0017

0.0010

–0.2188

0.5991

–0.2424

0.3867

Method 4

0.0032

0.0020

–0.4192

0.6177

–0.4049

0.4456

Method 5

0.0010

0.0011

0.3104

0.8103

0.1656

0.3594