Summary: A prevalence of heavy-tailed, peaked and skewed uncertainty phenomena have been cited in the literature dealing with economic, physics, and engineering data. This fact has invigorated the search for continuous distributions of this nature. In this paper we generalize the two-sided framework presented by S. Kotz
and J.R. van Dorp
[Beyond beta. Other continuous families of distributions with bounded support and applications. NJ: World Scient. Publ. (2004; Zbl 1094.62012
)] for the construction of families of distributions with bounded support via a mixture technique utilizing two generating densities instead of one. The family of Elevated Two-Sided Power (ETSP) distributions is studied as an instance of this generalized framework. Through a moment ratio diagram comparison, we demonstrate that the ETSP family allows for a remarkable flexibility when modeling heavy-tailed and peaked, but skewed uncertainty phenomena. We demonstrate its applicability via an illustrative example utilizing 2008 US income data.