We demonstrate how large classes of discrete and continuous statistical
distributions can be incorporated into coherent states, using the concept of a
reproducing kernel Hilbert space. Each family of coherent states is shown to
contain, in a sort of duality, which resembles an analogous duality in Bayesian
statistics, a discrete probability distribution and a discretely parametrized
family of continuous distributions. It turns out that nonlinear coherent
states, of the type widely studied in quantum optics, are a particularly useful
class of coherent states from this point of view, in that they contain many of
the standard statistical distributions. We also look at vector coherent states
and multidimensional coherent states as carriers of mixtures of probability
distributions and joint probability distributions