Journal of Probability and Statistics / 2010 / Article / Tab 3

Research Article

Zenga's New Index of Economic Inequality, Its Estimation, and an Analysis of Incomes in Italy

Table 3

Confidence intervals for 𝑍 𝐹 in the 2006 Italian income distribution.

 𝑍 𝑛 estimator  𝑍 𝑛 estimator
9 5 % 9 9 % 9 5 % 9 9 %
Lower Upper Lower Upper Lower Upper Lower Upper

Northwest ∢ 𝑛 = 1 9 8 8 ,  𝑍 𝑛 = 0 . 5 9 5 3 ,  𝑍 𝑛 = 0 . 5 9 4 8
Normal0.5775 0.61440.5717 0.62020.57710.61380.5713 0.6196
Student0.5786 0.61680.5737 0.62400.57910.61720.5748 0.6243
Percent0.5763 0.61320.5710 0.61930.57580.61240.5706 0.6185
BCa0.5789 0.61600.5741 0.62340.57850.61560.5738 0.6226

Northeast ∢ 𝑛 = 1 7 2 3 ,  𝑍 𝑛 = 0 . 6 1 0 8 ,  𝑍 𝑛 = 0 . 6 1 0 8
Normal0.5849 0.63930.5764 0.64780.58490.63930.5764 0.6479
Student0.5874 0.65260.5796 0.66690.58970.65380.5836 0.6685
Percent0.5840 0.63790.5773 0.64760.58390.63790.5772 0.6475
BCa0.5894 0.64780.5841 0.66160.58940.64790.5842 0.6615

Center ∢ 𝑛 = 1 5 7 4 ,  𝑍 𝑛 = 0 . 6 3 1 6 ,  𝑍 𝑛 = 0 . 6 3 1 6
Normal0.5957 0.67080.5839 0.68260.59560.67080.5838 0.6827
Student0.5991 0.69910.5897 0.72840.60360.70160.5977 0.7311
Percent0.5948 0.66890.5864 0.68180.59480.66880.5863 0.6818
BCa0.6024 0.68500.5963 0.70210.60240.68500.5963 0.7020

South ∢ 𝑛 = 1 6 2 0 ,  𝑍 𝑛 = 0 . 6 5 5 7 ,  𝑍 𝑛 = 0 . 6 5 4 3
Normal0.6358 0.67700.6293 0.68340.63460.67560.6282 0.6820
Student0.6371 0.68050.6313 0.69020.63710.67960.6320 0.6900
Percent0.6351 0.67570.6286 0.68280.63370.67420.6276 0.6812
BCa0.6375 0.67930.6325 0.68880.63630.67780.6315 0.6873

Islands ∢ 𝑛 = 8 6 1 ,  𝑍 𝑛 = 0 . 6 1 0 9 ,  𝑍 𝑛 = 0 . 6 0 9 5
Normal0.5918 0.63170.5856 0.63800.59100.63020.5848 0.6364
Student0.5927 0.63390.5864 0.64050.59280.63300.5874 0.6401
Percent0.5897 0.62970.5839 0.63600.58850.62750.5831 0.6340
BCa0.5923 0.63240.5868 0.64140.59140.63070.5860 0.6394

Italy (entire population) ∢ 𝑛 = 7 7 6 6 ,  𝑍 𝑛 = 0 . 6 4 7 0 ,  𝑍 𝑛 = 0 . 6 4 6 4
Normal0.6346 0.65960.6307 0.66360.63410.65910.6302 0.6630
Student0.6359 0.66290.6327 0.66860.63580.66270.6331 0.6683
Percent0.6348 0.65970.6314 0.66400.63430.65920.6309 0.6635
BCa0.6363 0.66190.6334 0.66760.63580.66130.6330 0.6669

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