Table 4 RE of memory-type exponential ratio and conventional exponential ratio estimators.

\(\:{\varvec{\uprho\:}}_{\mathbf{Y}\mathbf{X}}\)

n

\(\:\varvec{\lambda\:}=\:0.1\)

\(\:\varvec{\lambda\:}=\:0.2\)

\(\:\varvec{\lambda\:}=\:0.3\)

\(\:\varvec{\lambda\:}=\:0.5\)

\(\:\varvec{\lambda\:}=\:0.75\)

\(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}\)

\(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}^{\varvec{M}}\)

\(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}\)

\(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}^{\varvec{M}}\)

\(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}\)

\(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}^{\varvec{M}}\)

\(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}\)

\(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}^{\varvec{M}}\)

\(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}\)

\(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}^{\varvec{M}}\)

0.75

50

1.382

26.408

1.382

12.957

1.382

7.967

1.382

4.205

1.382

2.335

100

1.423

26.015

1.423

12.974

1.423

7.876

1.423

4.062

1.423

2.437

200

1.411

24.493

1.411

12.415

1.411

7.602

1.411

3.840

1.411

2.255

300

1.423

23.172

1.423

13.193

1.423

8.570

1.423

4.290

1.423

2.496

500

1.455

21.433

1.455

13.248

1.455

7.960

1.455

4.855

1.455

2.682

0.80

50

1.620

30.821

1.620

13.811

1.620

9.152

1.620

4.953

1.620

2.808

100

1.601

29.090

1.601

14.952

1.601

8.974

1.601

4.899

1.601

2.541

200

1.611

26.624

1.611

15.055

1.611

9.937

1.611

5.512

1.611

2.960

300

1.623

24.890

1.623

12.750

1.623

9.552

1.623

4.762

1.623

2.702

500

1.619

22.494

1.619

13.654

1.619

8.465

1.619

5.004

1.619

2.653

0.85

50

1.889

35.419

1.889

16.957

1.889

10.267

1.889

5.207

1.889

3.379

100

1.838

32.174

1.838

16.215

1.838

10.954

1.838

5.302

1.838

3.115

200

1.897

30.840

1.897

15.659

1.897

10.198

1.897

5.394

1.897

3.010

300

1.851

27.630

1.851

15.896

1.851

10.044

1.851

5.534

1.851

3.091

500

1.844

24.699

1.844

14.677

1.844

9.975

1.844

5.371

1.844

2.807

0.90

50

2.224

41.211

2.224

22.100

2.224

12.864

2.224

6.907

2.224

3.759

100

2.268

39.776

2.268

20.189

2.268

12.788

2.268

6.293

2.268

3.476

200

2.326

36.928

2.326

21.616

2.326

12.562

2.326

6.617

2.326

3.740

300

2.212

32.632

2.212

19.288

2.212

12.634

2.212

6.592

2.212

3.750

500

2.314

30.351

2.314

19.943

2.314

12.806

2.314

6.821

2.314

3.940

0.95

50

2.798

50.457

2.798

24.067

2.798

15.734

2.798

8.274

2.798

4.812

100

2.888

49.411

2.888

24.137

2.888

15.720

2.888

8.661

2.888

4.678

200

2.833

43.901

2.833

24.847

2.833

15.857

2.833

8.706

2.833

5.019

300

2.869

39.962

2.869

27.109

2.869

16.493

2.869

8.752

2.869

5.109

500

2.885

34.077

2.885

23.142

2.885

16.980

2.885

9.131

2.885

5.150