Table 1 Some members of the T-X family.

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

W\(\left( F(x)\right)\)

Rang of T

The family

Author

F(x)

(0, 1)

Beta G family

2

Kumaraswamy G family

3

\(-\log \left( 1-F^{\alpha }(x)\right)\)

\((0,\infty )\)

Exponentiated T-X family

4

\(\dfrac{-\log \left( 1-F(x)\right) }{1-F(x)}\)

\((0,\infty )\)

New Weibull-X family

5

\(\dfrac{-\log \left( 1-F^{\alpha }(x)\right) }{1-F^{\alpha }(x)}\)

\((0,\infty )\)

Jamal Weibull-X family

6

\(-\log \left( \dfrac{1-F(x)}{e^{F(x)}}\right)\)

\((0,\infty )\)

Weighted T-X family

7

\(X^{\theta }F(x)\)

(0, 1)

T-\(X^{\theta }\) family

Proposed

\((0,\infty )\)