Table 4 Mean and variance of the 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

\(\alpha\) = 2

\(\alpha\) = 7

\(\mu\)

\(\sigma ^{2}\)

\(\mu\)

\(\sigma ^{2}\)

\(\mu\)

\(\sigma ^{2}\)

\(\mu\)

\(\sigma ^{2}\)

\(\mu\)

\(\sigma ^{2}\)

\(\mu\)

\(\sigma ^{2}\)

0.9

2.438

2.406

1.687

1.457

1.445

1.283

1.358

1.248

1.179

1.251

1.070

1.340

1

2.285

1.838

1.599

1.098

1.373

0.949

1.291

0.915

1.119

0.904

1.015

0.975

3

1.406

0.165

1.161

0.119

1.066

0.106

1.028

0.102

0.943

0.096

0.894

0.103

5

1.240

0.059

1.090

0.048

1.028

0.044

1.000

0.043

0.948

0.042

0.918

0.043

10

1.110

0.015

1.040

0.013

1.010

0.013

0.996

0.012

0.960

0.013

0.951

0.013

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