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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
p ̂ 1 p ̂ 2 q ̂ p ̂ 1 p ̂ 2 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