In modeling statistical data by using entropy optimization distributions, the choice of a suitable moment function set and various combinations of their elements are very important. It is also important to have criteria to compare various moment sets for suitability. Considering this, in the present study, by choosing special moment function sets, we have obtained MaxMaxEnt, MinMaxEnt distributions and shown that the MinMaxEnt distribution more exactly represents the given statistical data. Moreover, in order to compare various moment function sets for suitability, we have suggested a new concept of relative suitability of moment function sets for given statistical data, and the importance of this concept has been presented in some applications using real data. (C) 2008 Elsevier Inc. All rights reserved.