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Table 6 Simulation from KwTP of the MLE for α=2,λ=0.1,a=3, and b=2.5

From: The Kumaraswamy transmuted Pareto distribution

Sample size

Parameter

Estimate

RMSE

MAE

(n)

    

5

\(\hat {\alpha }\)

2.0490

0.7727

0.6466

 

\(\hat {\lambda }\)

-0.1342

0.6446

0.5640

 

\(\hat {a}\)

2.7096

1.0869

0.8522

 

\(\hat {b}\)

2.4806

1.1296

0.9987

10

\(\hat {\alpha }\)

2.0722

0.6983

0.5810

 

\(\hat {\lambda }\)

-0.1046

0.6089

0.5274

 

\(\hat {a}\)

2.7421

0.9994

0.7871

 

\(\hat {b}\)

2.5427

1.0715

0.9389

20

\(\hat {\alpha }\)

2.0429

0.6157

0.5030

 

\(\hat {\lambda }\)

-0.0228

0.5786

0.5022

 

\(\hat {a}\)

2.8104

0.9036

0.7274

 

\(\hat {b}\)

2.5201

0.9400

0.8048

50

\(\hat {\alpha }\)

2.0078

0.5674

0.4486

 

\(\hat {\lambda }\)

0.0330

0.5507

0.4692

 

\(\hat {a}\)

2.8363

0.8251

0.6755

 

\(\hat {b}\)

2.4863

0.8682

0.7382

100

\(\hat {\alpha }\)

1.9644

0.5361

0.4302

 

\(\hat {\lambda }\)

0.0590

0.5288

0.4445

 

\(\hat {a}\)

2.8337

0.7392

0.5914

 

\(\hat {b}\)

2.4907

0.7856

0.6617

200

\(\hat {\alpha }\)

1.9783

0.5214

0.4246

 

\(\hat {\lambda }\)

0.0628

0.5082

0.4210

 

\(\hat {a}\)

2.8550

0.6567

0.5191

 

\(\hat {b}\)

2.5186

0.7352

0.6141

500

\(\hat {\alpha }\)

1.9691

0.5515

0.4607

 

\(\hat {\lambda }\)

0.0846

0.4972

0.4057

 

\(\hat {a}\)

2.8452

0.6056

0.4562

 

\(\hat {b}\)

2.5001

0.7121

0.5980

1000

\(\hat {\alpha }\)

1.9802

0.5694

0.4841

 

\(\hat {\lambda }\)

0.1073

0.4818

0.3830

 

\(\hat {a}\)

2.8629

0.5301

0.3895

 

\(\hat {b}\)

2.4704

0.6748

0.5693