  The internal disorder of the two-dimensional confined hydrogenic atom is
numerically studied in terms of the confinement radius for the 1\textit{s},
2\textit{s}, 2\textit{p} and 3\textit{d} quantum states by means of the
statistical Cr\'amer-Rao complexity measure. First, the confinement dependence
of the variance and the Fisher information of the position and momentum
spreading of its electron distribution are computed and discussed. Then, the
Cr\'amer-Rao complexity measure (which quantifies the combined balance of the
charge concentration around the mean value and the gradient content of the
electron distribution) is investigated in position and momentum spaces. We
found that confinement does distinguish complexity of the system for all
quantum states by means of this two component measure.
