$y>0$, that introduces a new parameter $\gamma>0$. This transformation is defined through the cumulative distribution function (CDF) $$\begin{aligned}
\label{MOdistribution}
G(y;\theta,\gamma)=\dfrac{ F(y;\theta)}{F(y;\theta)+\gamma(1-F(y;\theta))}.\end{aligned}$$

The interpretation of the parameter $\gamma$ is given in [@MO97] in terms of the behavior of the ratio of hazard rates of $F$ and $G$. This ratio is increasing in $y$ for $\gamma\geq 1$ and decreasing in $y$ for $0<\gamma\leq 1$. This transformation is then proposed for the exponential and Weibull distributions in [@MO97] in order to generate more flexible models for lifetime data. Clearly, for $\gamma=1$, $G$ and $F$ coincide. Many choices of $F(;\theta)$ have already been studied in the literature. We refer the reader to [@FS06] for a general mechanism for adding parameters to a distribution.

*Using transformations from ${\mathbb R}$ to ${\mathbb R}_+$*. The most common choice for this transformation is the exponential function. The idea is to define a positive variable $Y$ by transforming a real variable $X$ through $Y=\exp(X)$. This method is used to produce the class of log-symmetric distributions. This is, the family of positive random variables such that their logarithm is symmetrically distributed. Some members of this class are the lognormal, log-logistic, and log-Student-$t$ distributions, which are obtained by transforming the normal, 