Table 3 Empirical power for each method at significance level 0.05 with 10 ⁴ replicates from the simulation study

Uniform U(a,b)

(20,20,20)

a = (0,0,0.25), b = (1,1,1)

0.699

0.607

0.877

0.962

0.069

a = (0,0.1,0.1), b = (0.5,0.5,0.5)

0.450

0.339

0.724

0.830

0.726

a = (0.6,0.6,0.5), b = (1,1,1)

0.460

0.338

0.695

0.821

0.027

(15,20,25)

a = (0,0,0.25), b = (1,1,1)

0.809

0.692

0.926

0.980

0.957

a = (0,0.1,0.1), b = (0.5,0.5,0.5)

0.433

0.319

0.618

0.758

0.218

a = (0.6,0.6,0.5), b = (1,1,1)

0.482

0.380

0.754

0.854

0.860

Truncated Normal TN (μ, σ²)

(20,20,20)

μ = (0.1,0.1,0.2), σ = (1,1,1)/5

0.451

0.394

0.743

0.862

0.052

μ = (0.1,0.1,0.2), σ = (1,1.2,1.3)/5

0.773

0.642

0.962

0.954

0.200

μ = (0.5,0.5,0.4), σ = (1,1,1)/5

0.691

0.656

0.918

0.976

0.054

μ = (0.5,0.5,0.4), σ = (1,1.2,1.3)/5

0.402

0.374

0.696

0.820

0.032

(15,20,25)

μ = (0.1,0.1,0.2), σ = (1,1,1)/5

0.464

0.428

0.786

0.886

0.948

μ = (0.1,0.1,0.2), σ = (1,1.2,1.3)/5

0.735

0.643

0.959

0.952

0.713

μ = (0.5,0.5,0.4), σ = (1,1,1)/5

0.775

0.738

0.949

0.981

0.827

μ = (0.5,0.5,0.4), σ = (1,1.2,1.3)/5

0.382

0.364

0.756

0.838

0.852

Beta (c,d)

(20,20,20)

c = (1,1,1), d = (30,40,50)

0.596

0.442

0.889

0.723

0.432

c = (1,1.2,1.5), d = (40,40,40)

0.490

0.609

0.962

0.920

0.329

c = (30,40,50), d = (1,1,1)

0.578

0.450

0.899

0.745

0.420

c = (40,40,40), d = (1,1.2,1.5)

0.488

0.620

0.972

0.924

0.369

(15,20,25)

c = (1,1,1), d = (30,40,50)

0.608

0.405

0.861

0.727

0.998

c = (1,1.2,1.5), d = (40,40,40)

0.426

0.602

0.952

0.912

0.559

c = (30,40,50), d = (1,1,1)

0.618

0.409

0.888

0.752

0.458

c = (40,40,40), d = (1,1.2,1.5)

0.450

0.606

0.958

0.919

0.995