  We study the sample-to-sample fluctuations of the overlap probability
densities from large-scale equilibrium simulations of the three-dimensional
Edwards-Anderson spin glass below the critical temperature. Ultrametricity,
Stochastic Stability and Overlap Equivalence impose constraints on the moments
of the overlap probability densities that can be tested against numerical data.
We found small deviations from the Ghirlanda-Guerra predictions, which get
smaller as system size increases. We also focus on the shape of the overlap
distribution, comparing the numerical data to a mean-field-like prediction in
which finite-size effects are taken into account by substituting delta
functions with broad peaks
