. Author manuscript; available in PMC: 2011 May 1.

Published in final edited form as: Br J Math Stat Psychol. 2009 Sep 29;63(Pt 2):273–291. doi: 10.1348/000711009X449771

Table 3.

Kolmogorov-Smirnov (KS) distances and the mean KS (MKS) between the empirical distributions of the statistics and their proposed distributions, λ_d = (1, 1.1, 1.2, …, 1 + .1[d − d/10 − 1], 10, 20, …, d)′, 2000 replications.

		KS				MKS
d	CV(λ)	$χ_{d}^{2}$	$L χ_{d}^{2}$	$c χ_{d}^{2}$	$a χ_{b}^{2}$	$χ_{d}^{2}$	$L χ_{d}^{2}$	$c χ_{d}^{2}$	$a χ_{b}^{2}$
10	1.147	0.022	0.519	0.116	0.062	0.010	0.328	0.067	0.030
20	1.352	0.022	0.838	0.154	0.054	0.008	0.472	0.083	0.029
30	1.462	0.022	0.960	0.157	0.042	0.010	0.498	0.088	0.024
40	1.531	0.017	0.993	0.181	0.051	0.007	0.500	0.098	0.023
50	1.579	0.029	1.000	0.172	0.039	0.014	0.500	0.096	0.018
60	1.613	0.013	1.000	0.171	0.033	0.005	0.500	0.093	0.016
70	1.640	0.018	1.000	0.185	0.034	0.008	0.500	0.100	0.018
80	1.660	0.012	1.000	0.190	0.041	0.004	0.500	0.103	0.024
90	1.677	0.028	1.000	0.191	0.029	0.008	0.500	0.103	0.014
100	1.691	0.019	1.000	0.191	0.029	0.005	0.500	0.107	0.013
Ave	1.535	0.020	0.931	0.171	0.041	0.008	0.480	0.094	0.021

λ₁₀ = (1, 1.1, 1.2, …, 1.7, 1.8, 10)′, λ₂₀ = (1, 1.1, 1.2, …, 2.6, 2.7, 10, 20)′, …, λ₁₀₀ = (1, 1.1, 1.2, …, 9.7, 9.8, 9.9, 10, 20, 30, …, 100)′.