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Table 1 Some members of the T-X family

From: A new Weibull-X family of distributions: properties, characterizations and applications

W[F(x; ξ)] Range of X Members of 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 − Fα(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)