Journal of Statistical Distributions and Applications

Table 2 Parameter estimates for the BG models (with beta and GB1 marginals) fitted to the variables education & income by maximum likelihood (standard errors in parenthesis)

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

Variables: education & income
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	2.2431	3.3973	2.8809	2.1813	16.6110	2.6533	0.9603	0.2195
	(0.2008)	(0.3063)	(0.2591)	(0.5790)	(13.5230)	(0.2743)	(0.2243)	(0.1715)
1985	2.8775	3.7222	3.1934	4.3394	10.2173	2.7715	0.6321	0.3586
	(0.2572)	(0.3338)	(0.2858)	(1.4677)	(5.6252)	(0.2881)	(0.1955)	(0.1857)
1990	3.1691	3.6855	3.0715	6.4501	7.6217	2.6157	0.4702	0.4541
	(0.2834)	(0.3302)	(0.2746)	(2.7530)	(3.5058)	(0.2725)	(0.1880)	(0.1960)
1995	3.3196	3.3074	2.7070	6.3618	6.2069	2.3322	0.4907	0.4965
	(0.2978)	(0.2967)	(0.2421)	(2.4599)	(2.2291)	(0.2418)	(0.1818)	(0.1698)
2000	3.4652	3.0623	2.3826	5.8748	5.8042	2.0680	0.5420	0.4885
	(0.3119)	(0.2751)	(0.2131)	(2.2960)	(2.0882)	(0.2139)	(0.2052)	(0.1691)
2005	3.6366	2.8670	2.0777	7.2438	3.4311	1.8787	0.4773	0.7694
	(0.3285)	(0.2580)	(0.1858)	(3.2031)	(0.8872)	(0.1918)	(0.2070)	(0.1937)
2010	3.7596	2.7789	1.8944	3.4581	4.0863	1.8134	1.0309	0.6702
	(0.3406)	(0.2505)	(0.1693)	(1.0479)	(1.1725)	(0.1835)	(0.3034)	(0.1870)

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