  By using the Renyi entropy, and following the same scheme that in the
Fisher-Renyi entropy product case, a generalized statistical complexity is
defined. Several properties of it, including inequalities and lower and upper
bounds are derived. The hydrogen atom is used as a test system where to
quantify these two different statistical magnitudes, the Fisher-Renyi entropy
product and the generalized statistical complexity. For each level of energy,
both indicators take their minimum values on the orbitals that correspond to
the highest orbital angular momentum. Hence, in the same way as happens with
the Fisher-Shannon and the statistical complexity, these generalized Renyi-like
statistical magnitudes break the energy degeneration in the H-atom.
