Generalization of the Weibull distribution: the odd Weibull family

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Weibull Rayleigh Distribution: Theory and Applications (2015, unknown): “= 1− e { −α [ G(x;ζ ) G(x) ]β} , x ∈ R;α,β > 0, (3)”
Modeling Tree Diameter Distributions in Natural Forests: An Evaluation of 10 Statistical Models (2015, methodology): “Some of them have been derived from transformations of other models, such as the MW, OW, LL, and JSB (Lai et al. 2003, Wang and Rennolls 2005, Cooray 2006), making them more phenomenological than theoretical descriptions of diameter distributions.”
An Economic order quantity model for Items with Three-parameter Weibull distribution Deterioration, Ramp-type Demand and Shortages (2013, background): “Cooray [19] suggested that when modeling monotone hazard rates, the weibull distribution may be an initial choice because of its negatively and positively skewed density shape.”
Generalized Gumbel distribution (2010, methodology): “Consider the following odd Weibull distribution function [2], which originated from the idea of evaluating the odds of death of a Weibull or an inverse Weibull random variable.”
The Weibull-G Family of Probability Distributions (2014, background): “An interpretation of the Wei-G family of distributions can be given as follows (Cooray, 2006) in a similar context.”