  We introduce a general class of continuous univariate distributions with
positive support obtained by transforming the class of two-piece distributions.
We show that this class of distributions is very flexible, easy to implement,
and contains members that can capture different tail behaviours and shapes,
producing also a variety of hazard functions. The proposed distributions
represent a flexible alternative to the classical choices such as the
log-normal, Gamma, and Weibull distributions. We investigate empirically the
inferential properties of the proposed models through an extensive simulation
study. We present some applications using real data in the contexts of
time-to-event and accelerated failure time models. In the second kind of
applications, we explore the use of these models in the estimation of the
distribution of the individual remaining life.
