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. Author manuscript; available in PMC: 2013 Jul 19.

Published in final edited form as: Bernoulli (Andover). 2013;19(1):295–307. doi: 10.3150/11-BEJ393SUPP

Table 3.

Power comparison of tests for stochastic ordering of k = 3 distributions at level α = 0.05

Distributions			n₁ = n₂ = n₃ = 30		n₁ = n₂ = n₃ = 50
F₁	F₂	F₃	T_n	S_n	T_n	S_n
Uni(0, 1)	Uni(0, 1)	Uni(0, 1)	0.038	0.033	0.045	0.039
Uni(0, 1.1)	Uni(0, 1)	Uni(0, 1)	0.455	0.370	0.740	0.647
Uni(0, 1.1)	Uni(0, 1.1)	Uni(0, 1)	0.389	0.319	0.651	0.633
Uni(0.1, 1.1)	Uni(0, 1)	Uni(0, 1)	0.948	0.884	0.999	0.885
Exp(1)	Exp(1)	Exp(1)	0.041	0.019	0.049	0.045
Exp(1)	Exp(1)	Exp(1.1)	0.076	0.033	0.098	0.067
Exp(1)	Exp(1.1)	Exp(1.1)	0.067	0.029	0.098	0.073
Exp(1)	Exp(1.1)	Exp(1.2)	0.116	0.046	0.171	0.109
Exp(1)	Exp(1.25)	Exp(1.5)	0.313	0.121	0.507	0.321
N(0, 1)	N(0, 1)	N(0, 1)	0.042	0.035	0.049	0.035
N(0.1, 1)	N(0, 1)	N(0, 1)	0.272	0.183	0.423	0.292
N(0.1, 1)	N(0.1, 1)	N(0, 1)	0.246	0.151	0.393	0.249
N(0.5, 1)	N(0.25, 1)	N(0, 1)	1.000	0.993	1.000	1.000