  In this work, the calculation of a statistical measure of complexity and the
Fisher-Shannon information is performed for all the atoms in the periodic
table. Non-relativistic and relativistic cases are considered. We follow the
method suggested in [C.P. Panos, N.S. Nikolaidis, K. Ch. Chatzisavvas, C.C.
Tsouros, arXiv:0812.3963v1] that uses the fractional occupation probabilities
of electrons in atomic orbitals, instead of the continuous electronic wave
functions. For the order of shell filling in the relativistic case, we take
into account the effect due to electronic spin-orbit interaction. The
increasing of both magnitudes, the statistical complexity and the
Fisher-Shannon information, with the atomic number $Z$ is observed. The shell
structure and the irregular shell filling is well displayed by the
Fisher-Shannon information in the relativistic case.
