Table 1 Some members of the T-X family

F(x; ξ)

[0, 1]

Beta-G (Eugene et al., 2002), Mc-G (Alexander et al., 2012)

− log[F(x; ξ)]

(0, ∞)

Gamma-G Type-2 (Risti’c and Balakrishnan, 2012)

− log[1 − F(x; ξ)]

(0, ∞)

Gamma-G Type-1 (Zografos and Balakrishnan, 2009)

\( \frac{F\left(x;\xi \right)}{1-F\left(x;\xi \right)} \)

(0, ∞)

Gamma-G Type-3 (Torabi and Montazeri, 2012)

− log[1 − F^α(x; ξ)]

(0, ∞)

Exponentiated T-X (Alzaghal et al., 2013)

\( \log \left\{\frac{F\left(x;\xi \right)}{1-F\left(x;\xi \right)}\right\} \)

(−∞, ∞)

Logistic-G (Torabi and Montazeri, 2014)

log[− log {1 − F(x; ξ)}]

(−∞, ∞)

The Logistic-X Family (Tahir et al., 2015a, b)

\( \frac{\left[-\log \left\{1-F\left(x;\xi \right)\right\}\right]}{1-F\left(x;\xi \right)} \)

(0, ∞)

New Weibull-X Family (Proposed)