  The presence of a phase transition in a finite system can be deduced,
together with its order, from the shape of the distribution of the order
parameter. This issue has been extensively studied in multifragmentation
experiments, with results that do not appear fully consistent. In this paper we
discuss the effect of the statistical ensemble or sorting conditions on the
shape of fragment distributions, and propose a new method, which can be easily
implemented experimentally, to discriminate between different fragmentation
scenarii. This method, based on a reweighting of the measured distribution to
account for the experimental constraints linked to the energy deposit, is
tested on different simple models, and appears to provide a powerful
discrimination.
