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Table 3 Monte Carlo RMSEs and bias values of the entropy estimators VE ( m,n ) and AE ( m,n ) for the standard normal distribution, H(f) = 1.419

From: Goodness-of-fit testing for the inverse Gaussian distribution based on new entropy estimation using ranked set sampling and double ranked set sampling

n

m

SRS

RSS

  

VE (m,n)

AE (m,n)

VE (m,n)

AE (m,n)

  

Bias

RMSE

Bias

RMSE

Bias

RMSE

Bias

RMSE

10

1

−0.598925

0.676499

−0.538428

0.623068

−0.484489

0.549750

−0.429406

0.502967

 

2

−0.521455

0.591007

−0.409842

0.496627

−0.422169

0.471157

−0.308706

0.375690

 

3

−0.563002

0.623188

−0.386562

0.468471

−0.462240

0.504378

−0.291133

0.353844

 

4

−0.610651

0.663364

0.388846

0.469519

−0.523019

0.557792

−0.292810

0.351636

 

5

−0.671777

0.719069

−0.382242

0.461612

−0.584483

0.614209

−0.294820

0.349472

20

1

−0.435480

0.483459

−0.402721

0.452976

−0.382986

0.420310

−0.354315

0.393878

 

2

−0.327145

0.375798

−0.267005

0.324501

−0.275716

0.313472

−0.218758

0.264068

 

3

−0.317948

0.364927

−0.230598

0.292997

−0.268657

0.304811

−0.181588

0.230636

 

4

−0.327070

0.372436

−0.214227

0.279269

−0.285331

0.318855

−0.168035

0.219922

 

5

−0.352658

0.395796

−0.205782

0.272804

−0.305555

0.337744

−0.160392

0.213700

 

6

0.375996

0.416964

−0.203268

0.269194

−0.335066

0.365185

−0.162263

0.216405

 

7

−0.404050

0.442997

−0.200951

0.269828

−0.363782

0.391748

−0.162648

0.217866

 

8

−0.439618

0.475094

−0.203704

0.270603

−0.395221

0.421583

−0.163443

0.217711

 

9

−0.467134

0.500777

0.211872

0.276695

−0.428042

0.451680

−0.169841

0.224475

 

10

−0.496926

0.527456

−0.209085

0.275281

−0.454818

0.477152

−0.171572

0.224804

30

1

−0.378860

0.413455

−0.359097

0.394766

−0.343626

0.370512

−0.328056

0.355718

 

2

−0.259105

0.299687

−0.221750

0.266138

−0.226914

0.255947

−0.189446

0.223276

 

3

−0.236758

0.277238

−0.177599

0.229027

−0.204698

0.234358

−0.147274

0.186797

 

4

−0.234369

0.275867

−0.158560

0.213972

−0.204765

0.234413

−0.125487

0.169031

 

5

−0.244288

0.283027

−0.148610

0.206988

−0.214434

0.243683

−0.117590

0.165087

 

6

−0.255248

0.293332

−0.139542

0.200072

−0.227340

0.255901

−0.111407

0.161770

 

7

−0.269724

0.305134

−0.132038

0.196792

−0.241325

0.268228

−0.105796

0.158654

 

8

−0.285713

0.321039

−0.129915

0.193509

−0.254983

0.282376

−0.102504

0.157726

 

9

−0.304064

0.337563

−0.131105

0.198239

−0.274697

0.301420

−0.103392

0.160749

 

10

−0.320051

0.352764

−0.130086

0.196928

−0.295057

0.319933

−0.101392

0.160593

 

11

−0.339131

0.369866

−0.127890

0.196985

−0.314201

0.339141

−0.102034

0.161378

 

12

−0.361226

0.392070

−0.130212

0.197655

−0.333173

0.356224

−0.103026

0.163577

 

13

−0.382347

0.410463

0.129885

0.199488

−0.353582

0.375170

−0.105978

0.165825

 

14

−0.400618

0.428008

−0.131518

0.199794

−0.375752

0.397462

−0.109190

0.168154

 

15

−0.423597

0.449968

−0.134062

0.200285

−0.394363

0.414605

−0.108705

0.167780