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Table 1 Power comparisons for a one-sided rank test H 0 :F ( x ; θ o , σ o ) = G ( x ; θ a , σ a ) v.s. H a :Fk( x ; θ o , σ o ) = G ( x ; θ a , σ a )

From: Joint distribution of rank statistics considering the location and scale parameters and its power study

  

m= 6 n= 10

m= 10 n= 10

m= 10 n= 20

 F

Test

β(F)

β(F2)

β(F3)

β(F6)

β(F)

β(F2)

β(F3)

β(F6)

β(F)

β(F2)

β(F3)

β(F6)

U(0,1)

R l

.090

.411

.647

.900

.096

.496

.761

.967

.099

.591

.845

.984

 

R s

.080

.152

.193

.218

.076

.137

.149

.123

.100

.236

.370

.638

 

R l &R s

.100

.452

.699

.934

.100

.531

.799

.981

.100

.622

.878

.992

t(3)

R l

0.090

.412

.639

.897

0.096

.493

.756

.965

0.099

.574

.841

.987

 

R s

0.080

.150

.197

.217

0.076

.137

.152

.121

0.100

.234

.367

.634

 

R l &R s

0.100

.453

.696

.932

0.100

.528

.798

.980

0.100

.606

.874

.993

E x p(1)

R l

0.090

.411

.650

.899

0.096

.490

.764

.967

0.099

.579

.841

.987

 

R s

0.080

.149

.195

.217

0.076

.140

.152

.122

0.100

.232

.376

.641

 

R l &R s

0.100

.451

.702

.933

0.100

.525

.805

.982

0.100

.607

.875

.993

  1. Note: A sectorial critical region is chosen for a simultaneous testing.