A method, which we suggest to call the Empirical Maximum Entropy method, is implicitly present at Maximum Entropy Empirical Likelihood method, as its special, non-parametric case. From this vantage point the entropy-based empirical approach to estimation is surveyed.

The game which can be taken to lie behind the maximum entropy principle is studied. Refining previous techniques, we present a comprehensive and satisfactory theoretical discussion of the fundamentals of this game in its simplest setting. The results are illustrated by concrete examples pertaining to well known classical models.

Based on the principle of maximum entropy the primary morphologic equation is derived, and then the equations for hydraulic geometry of longitudinal profile and crosssection are established. For V-shaped cross-sections the relevant morphologic equations which are derived are compared with the existing empirical and semi-empirical formulae. They show good agreement with the prototypes.