Deriving physical parameters of unresolved star clusters IV. The M33
  star cluster system
  Context. When trying to derive the star cluster physical parameters of the
M33 galaxy using broad-band unresolved ground-based photometry, previous
studies mainly made use of simple stellar population models, shown in the
recent years to be oversimplified.
  Aims. In this study, we aim to derive the star cluster physical parameters
(age, mass, and extinction; metallicity is assumed to be LMC-like for clusters
with age below 1\,Gyr and left free for older clusters) of this galaxy using
models that take stochastic dispersion of cluster integrated colors into
account.
  Methods. We use three recently published M33 catalogs of cluster optical
broad-band photometry in standard $UBVRI$ and in CFHT/MegaCam $u^{*}g'r'i'z'$
photometric systems. We also use near-infrared $JHK$ photometry that we derive
from deep 2MASS images. We derive the cluster parameters using a method that
takes into account the stochasticity problem, presented in previous papers of
this series.
  Results. The derived differential age distribution of the M33 cluster
population is composed of a two-slope profile indicating that the number of
clusters decreases when age gets older. The first slope is interpreted as the
evolutionary fading phase of the cluster magnitudes, and the second slope as
the cluster disruption. The threshold between these two phases occurs at
$\sim$300\,Myrs, comparable to what is observed in the M31 galaxy. We also
model by use of artificial clusters the ability of the cluster physical
parameter derivation method to correctly derive the two-slope profile for
different photometric systems tested.
