The derivation of mathematical models accounting for the variation of physical properties along the thickness of thin systems such as oxide films, organic coatings and biological tissues, has been a challenging problem addressed for decades. Most attention has been paid to electrical resistivity because it typically undergoes a variation over several orders of magnitude, which is a necessary premise to explain the frequency dispersion over several decades of frequency observed in the impedance response of films. In this work we present a new distribution function for the spatial variation of resistivity within films, which is derived from the probability distribution that gives rise to exact constant-phase element (CPE) behavior. We demonstrate that this resistivity profile encompasses a wide variety of impedance behaviors including the probably most addressed types of frequency dispersion in films: the Young model and the CPE, thereby revealing an unknown relationship between them. These properties point to that distribution function as a promising fitting model for impedance data interpretation. In addition, the conditions for its applicability to real systems allowed us to postulate a lower bound for the CPE exponent as function of film properties which seems to be consistent with the values reported in the literature. (C) 2017 Elsevier Ltd. All rights reserved.