When was the last time you needed an asymmetric (skewed) probability density function (pdf) with infinite support? Traditional skewed distributions like the gamma family suffer from a semi-infinite support, that is, . The support, if you are out of the loop, is the set of values in the domain of such that . Why is this inconvenient? well, I will give more details about the specific application later, meanwhile, let’s say that the fact that its derivative is discontinuous at is problematic; even more, I need my function to be at least in , that is, to have at least continuous derivatives!.
This post constitutes a somewhat dirty solution being as unwilling as I am to review any literature in depth (I might be inventing the wheel again, some wheel, but who cares; this is a blog!). Here we go.