set of covariates (see *e.g.* [@L03]). Other areas where positive observations appear naturally are finance (*e.g.* in modelling the size of reinsurance claims), network traffic modelling [@M01], reliability theory [@ME98], environmental science [@MG10], among many others. Parametric distributions provide a parsimonious way of describing the distribution of those quantities. Some of the most popular choices for modelling positive observations are the lognormal, log-logistic, Gamma, and Weibull distributions. We refer the readers to [@M12] for an extensive overview of these sorts of distributions as well as a study of their inferential properties in the presence of censored observations. However, these distributions do not always provide a good fit of the data. For example, when the data present heavier tails and/or a different shape around the mode than those captured by these distributions. In recent years, there has been an increasing interest in the development of flexible distributions with positive support in order to cover departures from the classical choices. Two popular strategies for generating new flexible distributions with positive support consist of:

*Adding a shape parameter to an existing distribution with positive support*. For instance, in the context of reliability and survival analysis, [@MO97] proposed a transformation of a distribution $F(y;\theta)$, 