Table 3 ECPs of various confidence intervals under bivariate normal distribution with different ρ and δ, μ ₁, \(\mu _{2} {\sigma _{1}^{2}}\) and (n,n ₁,n ₂)=(5,2,2) and \({\sigma _{2}^{2}}=4\)

-0.9

1

-0.25

0

0.25

0.9390

0.9590

0.9370

0.9350

0.8800

0.9520

0.9560

0.9370

0.9570

0

1

1

0.9440

0.9580

0.9470

0.9220

0.8760

0.9470

0.9490

0.9300

0.9490

0.5

2

1.5

0.9430

0.9670

0.9530

0.9400

0.8860

0.9470

0.9480

0.9310

0.9480

8

-0.25

0

0.25

0.9410

0.9630

0.9450

0.9180

0.8600

0.9430

0.9490

0.9340

0.9490

0

1

1

0.9370

0.9580

0.9350

0.9240

0.8640

0.9510

0.9500

0.9390

0.9500

0.5

2

1.5

0.9380

0.9570

0.9410

0.9240

0.8750

0.9570

0.9560

0.9470

0.9560

-0.5

1

-0.25

0

0.25

0.9440

0.9610

0.9530

0.9200

0.8570

0.9490

0.9430

0.9330

0.9420

0

1

1

0.9420

0.9660

0.9230

0.9270

0.8660

0.9570

0.9560

0.9460

0.9550

0.5

2

1.5

0.9460

0.9660

0.9380

0.9250

0.8640

0.9480

0.9560

0.9430

0.9540

8

-0.25

0

0.25

0.9290

0.9590

0.9480

0.9230

0.8730

0.9470

0.9450

0.9390

0.9440

0

1

1

0.9290

0.9560

0.9420

0.9210

0.8790

0.9460

0.9430

0.9380

0.9440

0.5

2

1.5

0.9350

0.9690

0.9410

0.9330

0.8880

0.9520

0.9540

0.9470

0.9520

-0.1

1

-0.25

0

0.25

0.9300

0.9570

0.9500

0.9170

0.8630

0.9550

0.9500

0.9450

0.9470

0

1

1

0.9380

0.9590

0.9450

0.9170

0.8600

0.9540

0.9500

0.9450

0.9520

0.5

2

1.5

0.9400

0.9620

0.9440

0.9140

0.8560

0.9510

0.9460

0.9420

0.9460

8

-0.25

0

0.25

0.9460

0.9600

0.9310

0.9050

0.8490

0.9460

0.9470

0.9440

0.9470

0

1

1

0.9450

0.9670

0.9440

0.9150

0.8590

0.9560

0.9500

0.9480

0.9510

0.5

2

1.5

0.9350

0.9610

0.9360

0.9150

0.8570

0.9500

0.9520

0.9440

0.9490

0

1

-0.25

0

0.25

0.9380

0.9610

0.9400

0.9330

0.8860

0.9550

0.9550

0.9530

0.9530

0

1

1

0.9290

0.9610

0.9280

0.9200

0.8680

0.9470

0.9480

0.9470

0.9470

0.5

2

1.5

0.9300

0.9580

0.9420

0.9230

0.8800

0.9520

0.9510

0.9500

0.9510

8

-0.25

0

0.25

0.9210

0.9590

0.9390

0.9090

0.8400

0.9430

0.9450

0.9450

0.9450

0

1

1

0.9240

0.9570

0.9400

0.9050

0.8520

0.9430

0.9440

0.9430

0.9430

0.5

2

1.5

0.9360

0.9680

0.9380

0.9140

0.8540

0.9530

0.9530

0.9530

0.9520

0.1

1

-0.25

0

0.25

0.9310

0.9690

0.9480

0.9150

0.8530

0.9510

0.9510

0.9490

0.9490

0

1

1

0.9330

0.9670

0.9440

0.9150

0.8550

0.9500

0.9500

0.9490

0.9510

0.5

2

1.5

0.9310

0.9570

0.9490

0.9150

0.8630

0.9520

0.9520

0.9510

0.9520

8

-0.25

0

0.25

0.9220

0.9520

0.9420

0.9190

0.8700

0.9510

0.9510

0.9520

0.9520

0

1

1

0.9290

0.9540

0.9360

0.9210

0.8690

0.9490

0.9490

0.9470

0.9470

0.5

2

1.5

0.9180

0.9530

0.9350

0.9340

0.8860

0.9520

0.9520

0.9500

0.9500

0.5

1

-0.25

0

0.25

0.9230

0.9530

0.9470

0.8980

0.8470

0.9540

0.9540

0.9530

0.9530

0

1

1

0.9330

0.9620

0.9390

0.9050

0.8510

0.9440

0.9440

0.9440

0.9440

0.5

2

1.5

0.9280

0.9640

0.9330

0.9140

0.8640

0.9520

0.9520

0.9500

0.9500

8

-0.25

0

0.25

0.9360

0.9660

0.9420

0.9030

0.8450

0.9470

0.9470

0.9460

0.9460

0

1

1

0.9220

0.9600

0.9350

0.9060

0.8410

0.9500

0.9500

0.9480

0.9480

0.5

2

1.5

0.9300

0.9650

0.9500

0.9140

0.8570

0.9580

0.9580

0.9570

0.9570

0.9

1

-0.25

0

0.25

0.9190

0.9540

0.9400

0.9300

0.8710

0.9450

0.9450

0.9440

0.9430

0

1

1

0.9390

0.9640

0.9460

0.9360

0.8870

0.9590

0.9580

0.9570

0.9580

0.5

2

1.5

0.9240

0.9610

0.9310

0.9220

0.8760

0.9470

0.9460

0.9470

0.9470

8

-0.25

0

0.25

0.9200

0.9590

0.9440

0.9050

0.8440

0.9440

0.9430

0.9430

0.9450

0

1

1

0.9310

0.9620

0.9430

0.9040

0.8390

0.9450

0.9450

0.9460

0.9460

0.5

2

1.5

0.9310

0.9620

0.9400

0.9190

0.8610

0.9530

0.9520

0.9520

0.9530