Journal of Statistical Distributions and Applications

Table 8 Confidence Intervals (95%) for the BG models (with beta and GB1 marginals) fitted to the variables education & income 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	1.8495	2.7970	2.3731	1.0465	-9.8941	2.1157	0.5207	-0.1166
	Upper	2.6367	3.9976	3.3887	3.3161	43.1161	3.1909	1.3999	0.5556
1985	Lower	2.3734	3.0680	2.6332	1.4627	-0.8081	2.2068	0.2489	-0.0054
	Upper	3.3816	4.3764	3.7536	7.2161	21.2427	3.3362	1.0153	0.7226
1990	Lower	2.6136	3.0383	2.5333	1.0542	0.7503	2.0816	0.1017	0.0699
	Upper	3.7246	4.3327	3.6097	11.8460	14.4931	3.1498	0.8387	0.8383
1995	Lower	2.7359	2.7259	2.2325	1.5404	1.8379	1.8583	0.1344	0.1637
	Upper	3.9033	3.8889	3.1815	11.1832	10.5759	2.8061	0.8470	0.8293
2000	Lower	1.0808	0.8424	0.5077	13.4885	12.1203	0.4423	0.1112	0.0826
	Upper	4.0765	3.6015	2.8003	10.3750	9.8971	2.4872	0.9442	0.8199
2005	Lower	2.9927	2.3613	1.7135	0.9657	1.6922	1.5028	0.0716	0.3897
	Upper	4.2805	3.3727	2.4419	13.5219	5.1700	2.2546	0.8830	1.1491
2010	Lower	3.0920	2.2879	1.5626	1.4042	2.5649	1.4537	0.4362	0.3037
	Upper	4.4272	3.2699	2.2262	5.5120	7.1611	2.1731	1.6256	1.0367

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