Journal of Statistical Distributions and Applications

Table 7 Confidence intervals (95%) for the BG models (with beta and GB1 marginals) fitted to the variables education & 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
Year	Limit	${\hat{p}}_{1}$	${\hat{p}}_{2}$	$\hat{q}$	${\hat{p}}_{1}$	${\hat{p}}_{2}$	$\hat{q}$	$â_{1}$	$â_{2}$
1980	Lower	2.1890	5.8129	2.8324	4.6480	5.7359	2.0987	0.0234	0.2835
	Upper	3.1134	8.2959	4.0330	40.4710	15.3533	3.2315	0.2120	0.7927
1985	Lower	2.4261	6.2292	2.6925	3.9300	2.0665	2.0660	0.0924	0.0657
	Upper	3.4507	8.8870	3.8317	18.4094	26.5305	3.1676	0.4130	0.8175
1990	Lower	2.4208	5.8737	2.3475	-12.7571	3.2632	1.8294	-0.0498	0.4170
	Upper	3.4458	8.3865	3.3409	65.9835	10.1106	2.7988	0.2638	1.2962
1995	Lower	2.3508	5.0813	1.9290	3.5295	2.5792	1.6089	0.0334	0.6382
	Upper	3.3508	7.2655	2.7464	31.1215	6.3964	2.4419	0.2878	1.6526
2000	Lower	0.6984	2.8142	0.3379	7.9680	16.3910	0.3195	0.1146	0.3637
	Upper	3.2789	6.5616	2.2867	7.9990	11.3374	2.1194	0.9624	1.6891
2005	Lower	2.1839	4.1167	1.2959	-1.3359	1.3340	1.2329	-0.0203	1.1240
	Upper	3.1239	5.9109	1.8451	27.6623	3.3434	1.8515	0.4395	2.8704
2010	Lower	2.1865	4.2900	1.1606	1.1016	0.9017	1.1305	0.2577	0.3451
	Upper	3.1317	6.1692	1.6522	5.7210	6.5705	1.6863	1.3201	2.4191

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