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Table 1 Median, mean, variance, skewness, kurtosis for selected values of the parameters

From: The Kumaraswamy transmuted Pareto distribution

α

λ

a

b

Median

Mean

Variance

Skewness

Kurtosis

5

0.2

1

1

0.5636

0.6111

0.0224

4.9196

81.8250

6

0.2

1

1

0.5525

0.5891

0.0130

4.0458

42.9488

7

0.2

1

1

0.5446

0.5744

0.0084

3.5980

30.9806

8

0.2

1

1

0.5388

0.5638

0.0059

3.3243

25.2955

10

0.2

1

1

0.5309

0.5497

0.0034

3.0056

19.8668

5

-1

1

1

0.6392

0.6944

0.0386

4.1113

60.5271

5

-0.5

1

1

0.6061

0.6997

0.0335

4.2366

63.3030

5

0.1

1

1

0.5688

0.6181

0.0243

4.7743

77.4267

5

0.5

1

1

0.5505

0.5903

0.0162

5.4825

101.8249

5

0.8

1

1

0.5408

0.5694

0.0091

6.0430

135.7943

5

1

1

1

0.5359

0.5556

0.0039

2.8111

17.8286

5

0.5

1

1

0.5505

0.5903

0.0162

5.4825

101.8249

5

0.5

2

1

0.5964

0.6422

0.0249

4.7467

78.6519

5

0.5

3

1

0.6304

0.6802

0.0313

4.4534

70.3107

5

0.5

4

1

0.6578

0.7106

0.0366

4.2881

65.8432

5

0.5

5

1

0.6810

0.7362

0.0411

4.1793

63.0006

5

0.2

1

1

0.5636

0.6111

0.0224

4.9196

81.8250

5

0.2

1

2

0.5303

0.5480

0.0031

3.0122

20.2613

5

0.2

1

3

0.5199

0.5305

0.0011

2.6351

15.2360

5

0.2

1

4

0.5150

0.5224

0.0006

2.4635

13.3142

5

0.2

1

5

0.5118

0.5176

0.0003

2.3646

12.2905