Journal of Statistical Distributions and Applications

Table 3 Parameter estimates for the BG models (with beta and GB1 marginals) fitted to the variables income & health by maximum likelihood (standard errors in parenthesis)

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

Variables: income & health
Year	BG model with beta marginals			BG model with GB1 marginals
Year	${\hat{p}}_{1}$	${\hat{p}}_{2}$	$\hat{q}$	${\hat{p}}_{1}$	${\hat{p}}_{2}$	$\hat{q}$	$â_{1}$	$â_{2}$
1980	3.4799	5.9823	2.9491	7.2415	4.5699	2.7798	0.4964	1.1929
	(0.3103)	(0.5360)	(0.2624)	(2.1497)	(1.0817)	(0.2855)	(0.1417)	(0.2674)
1985	3.8895	7.7393	3.3336	19.9607	7.1397	2.7940	0.1918	0.9025
	(0.3458)	(0.6913)	(0.2959)	(11.3280)	(1.8739)	(0.2993)	(0.1072)	(0.2316)
1990	3.7983	8.0223	3.1630	19.2882	10.1747	2.5143	0.18067	0.63504
	(0.3379)	(0.7173)	(0.2808)	(10.8390)	(3.4854)	(0.2721)	(0.1003)	(0.2148)
1995	3.4082	7.5345	2.7867	12.4184	11.5787	2.2338	0.2457	0.5300
	(0.3039)	(0.6760)	(0.2478)	(4.6027)	(4.5656)	(0.2401)	(0.0901)	(0.2104)
2000	3.0781	7.0973	2.3944	11.9092	7.5709	1.9876	0.2346	0.7667
	(0.2752)	(0.6396)	(0.2132)	(4.7419)	(2.2840)	(0.2109)	(0.0935)	(0.2342)
2005	2.7891	6.8378	2.0250	19.9351	4.0164	1.7675	0.1323	1.4058
	(0.2501)	(0.6197)	(0.1805)	(19.3729)	(1.2603)	(0.1863)	(0.1265)	(0.4381)
2010	2.4296	6.5389	1.6754	4.4081	4.2348	1.5941	0.5388	1.4186
	(0.2188)	(0.5974)	(0.1496)	(1.2981)	(1.4324)	(0.1627)	(0.1582)	(0.4772)

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