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Table 1 Parameter estimates for the BG models (with beta and GB1 marginals) fitted to the variables education & health by maximum likelihood (standard errors in parenthesis)

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

 Variables: education & health

Year

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

2.6512

7.0544

3.4327

22.5595

10.5446

2.6651

0.1177

0.5381

 

(0.2358)

(0.6334)

(0.3063)

(9.1385)

(2.4534)

(0.2890)

(0.0481)

(0.1299)

1985

2.9384

7.5581

3.2621

11.1697

14.2985

2.6168

0.2527

0.4416

 

(0.2614)

(0.6780)

(0.2906)

(3.6937)

(6.2408)

(0.2810)

(0.0818)

(0.1918)

1990

2.9333

7.1301

2.8442

26.6132

6.6869

2.3141

0.1070

0.8566

 

(0.2615)

(0.6410)

(0.2534)

(20.0869)

(1.7468)

(0.2473)

(0.0800)

(0.2243)

1995

2.8508

6.1734

2.3377

17.3255

4.4878

2.0254

0.1606

1.1454

 

(0.2551)

(0.5572)

(0.2085)

(7.0388)

(0.9738)

(0.2125)

(0.0649)

(0.2588)

2000

2.7879

5.5716

1.9464

4.6151

5.7575

1.7644

0.5647

0.8677

 

(0.2505)

(0.5051)

(0.1736)

(1.7265)

(2.8469)

(0.1811)

(0.2029)

(0.4191)

2005

2.6539

5.0138

1.5705

13.1632

2.3387

1.5422

0.2096

1.9972

 

(0.2398)

(0.4577)

(0.1401)

(7.3975)

(0.5126)

(0.1578)

(0.1173)

(0.4455)

2010

2.6591

5.2296

1.4064

3.4113

3.7361

1.4084

0.7889

1.3821

 

(0.2411)

(0.4794)

(0.1254)

(1.1784)

(1.4461)

(0.1418)

(0.2710)

(0.5291)