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Table 9 Confidence intervals (95%) for the BG models (with beta and GB1 marginals) fitted to the variables income & health by maximum likelihood

From: Bivariate beta-generated distributions with applications to well-being data

 Variables: education & health

Year

Limit

BG model with beta marginals

BG model with GB1 marginals

p ̂ 1

p ̂ 2

q ̂

p ̂ 1

p ̂ 2

q ̂

â 1

â 2

1980

Lower

2.8717

4.9317

2.4348

3.0281

2.4498

2.2202

0.2187

0.6688

 

Upper

4.0881

7.0329

3.4634

11.4549

6.6900

3.3394

0.7741

1.7170

1985

Lower

3.2117

6.3844

2.7536

-2.2422

3.4669

2.2074

-0.0183

0.4486

 

Upper

4.5673

9.0942

3.9136

42.1636

10.8125

3.3806

0.4019

1.3564

1990

Lower

3.1360

6.6164

2.6126

-1.9562

3.3433

1.9810

-0.0159

0.2140

 

Upper

4.4606

9.4282

3.7134

40.5326

17.0061

3.0476

0.3773

1.0560

1995

Lower

2.8126

6.2095

2.3010

3.3971

2.6301

1.7632

0.0691

0.1176

 

Upper

4.0038

8.8595

3.2724

21.4397

20.5273

2.7044

0.4223

0.9424

2000

Lower

0.8471

4.5394

0.5105

56.4722

17.2919

0.4192

0.0219

0.1796

 

Upper

3.6175

8.3509

2.8123

21.2033

12.0475

2.4010

0.4179

1.2257

2005

Lower

2.2989

5.6232

1.6712

-18.0358

1.5462

1.4024

-0.1156

0.5471

 

Upper

3.2793

8.0524

2.3788

57.9060

6.4866

2.1326

0.3802

2.2645

2010

Lower

2.0008

5.3680

1.3822

1.8638

1.4273

1.2752

0.2287

0.4833

 

Upper

2.8584

7.7098

1.9686

6.9524

7.0423

1.9130

0.8489

2.3539