In this article, we propose a new generator of distributions based on a polynomial-exponential transformation of an existing cumulative distribution function. It naturally arises when we deal with parallel-series systems. We study some of its mathematical properties, including moments, a moment generating function, some measures of uncertainty, and a distribution of order statistics. Maximum likelihood estimation along with an extensive simulation study is discussed. The applicability of some submodels of the family is illustrated by means of two hydrologic data sets over existing distributions.