  The modeling of complex atomic spectra is a difficult task, due to the huge
number of levels and lines involved. In the presence of a magnetic field, the
computation becomes even more difficult. The anomalous Zeeman pattern is a
superposition of many absorption or emission profiles with different Zeeman
relative strengths, shifts, widths, asymmetries and sharpnesses. We propose a
statistical approach to study the effect of a magnetic field on the broadening
of spectral lines and transition arrays in atomic spectra. In this model, the
sigma and pi profiles are described using the moments of the Zeeman components,
which depend on quantum numbers and Land\'{e} factors. A graphical calculation
of these moments, together with a statistical modeling of Zeeman profiles as
expansions in terms of Hermite polynomials are presented. It is shown that the
procedure is more efficient, in terms of convergence and validity range, than
the Taylor-series expansion in powers of the magnetic field which was suggested
in the past. Finally, a simple approximate method to estimate the contribution
of a magnetic field to the width of transition arrays is proposed. It relies on
our recently published recursive technique for the numbering of LS-terms of an
arbitrary configuration.
