The search of an appropriate measure of relative complexity among density functions is afforded. In doing so, the main properties required for complexity functionals of a given distribution, as well as those for discrimination measures among two or more distributions are considered. A proposal for a generalized relative complexity is provided, enclosing a pioneering definition as a limiting case. A theoretical analysis of the generalized measure for arbitrary distributions is carried out. The applications regard the electron charge densities of neutral atoms, and the results are interpreted on the basis of the main physical properties of the systems considered. (C) 2012 Elsevier B.V. All rights reserved.