Duality in a maximum generalized entropy model.

This paper discusses a possible generalization for the maximum entropy principle. A class of generalized entropy is introduced by that of generator functions, in which the maximum generalized distribution model is explicitly derived including q-Gaussian distributions, Wigner semicircle distributions and Pareto distributions. We define a totally geodesic subspace in the total space of all probability density functions in a framework of information geometry. The model of maximum generalized entropy distributions is shown to be totally geodesic. The duality of the model and the estimation in the maximum generalized principle is elucidated to give intrinsic understandings from the point of information geometry. [ABSTRACT FROM AUTHOR]