On the distribution of Gini’s rank association index

Figures & data

Table 1. Asymptotic relative efficiency in the bivariate normal case.

Correlation coefficient	Asymptotic relative efficiency
Spearman’s rank correlation coefficient	${(\frac{3}{\pi })}^2$
Kendall’s rank correlation coefficient	${(\frac{3}{\pi })}^2$
Spearman’s footrule	$\frac{5}{6}{(\frac{3}{\pi })}^2$
Gini’s rank association index	$\frac{8}{9}{(\frac{3}{\pi })}^2$

Table 2. The calculated CDF of Gini’s gamma for n = 28 with the normal and Edgeworth approximations.

m	Calculated CDF	Normal approximation	Edgeworth approximation	m	Calculated CDF	Normal approximation	Edgeworth approximation
0	0.50637	0.50647	0.50637	160	0.99622	0.99548	0.99616
10	0.56967	0.57078	0.56969	170	0.99784	0.99722	0.99780
20	0.63129	0.63326	0.63133	180	0.99881	0.99833	0.99879
30	0.68980	0.69239	0.68986	190	0.99938	0.99902	0.99937
40	0.74399	0.74690	0.74407	200	0.99969	0.99944	0.99970
50	0.79293	0.79586	0.79303	210	0.99986	0.99969	0.99987
60	0.83603	0.83868	0.83613	220	0.99994	0.99983	0.99995
70	0.87301	0.87517	0.87311	230	0.99997	0.99991	0.99999
80	0.90392	0.90546	0.90399	240	0.99999	0.99995	1.00000
90	0.92906	0.92996	0.92911	250	1.00000	0.99998	1.00001
100	0.94896	0.94925	0.94896	260	1.00000	0.99999	1.00001
110	0.96425	0.96405	0.96423	270	1.00000	0.99999	1.00000
120	0.97567	0.97511	0.97562	280	1.00000	1.00000	1.00000
130	0.98394	0.98317	0.98387	…	…	…	…
140	0.98973	0.98888	0.98965	490	1.00000	1.00000	1.00000
150	0.99365	0.99282	0.99358