Table 5 Skewness and kurtosis of E-X\(^{\theta }\)E distribution for some values of \(\alpha\), and \(\theta\).

From: A new (T-X\(^\theta\)) family of distributions: properties, discretization and estimation with applications

\(\theta\)

\(\alpha = 0.2\)

\(\alpha = 0.5\)

\(\alpha = 0.8\)

\(\alpha = 1\)

\(\alpha = 5\)

\(\alpha = 7\)

Sk

Ku

Sk

Ku

Sk

Ku

Sk

Ku

Sk

Ku

Sk

Ku

0.9

1.21

5.34

1.71

8.27

2.06

10.52

2.20

11.43

2.42

12.07

2.40

11.87

1

1.03

4.53

1.39

6.32

1.68

7.88

1.81

8.60

2.08

9.45

2.05

9.28

3

− 0.04

2.74

0.01

2.75

0.05

2.75

0.08

2.75

0.20

2.74

0.19

2.72

5

− 0.35

3.01

− 0.33

2.98

− 0.31

2.96

− 0.29

2.95

− 0.24

2.85

− 0.24

2.86

10

− 0.67

3.65

− 0.66

3.63

− 0.65

3.62

− 0.65

3.61

− 0.63

3.55

− 0.63

3.56

Back to article page