  Husimi distributions and Wigner distributions are well-known
quasi-probability distributions which appear in several contexts. In this
paper, we show some remarkable aspects of these distribution functions related
to geometric structures of generalized coherent state systems and operational
quantum physics, and a scheme of formulating generalized version of
quasi-probability distributions. Our scheme gives concrete formulae of
quasi-probability distributions in more direct way from the theory of coherent
state systems and clarify their operational meanings, especially of Husimi
distributions and mutual relation between Husimi distributions and other
classes of quasi-probability distributions.
