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Concept of exponential family is generalized by simple and generalexponential form. Simple and general potential are introduced. Maximum Entropyand Maximum Likelihood tasks are defined. ML task on the simple exponentialform and ME task on the simple potentials are proved to be complementary inset-up and identical in solutions. ML task on the general exponential form andME task on the general potentials are weakly complementary, leading to the samenecessary conditions. A hypothesis about complementarity of ML and MiniMaxEntropy tasks and identity of their solutions, brought up by a special caseanalytical as well as several numerical investigations, is suggested in thiscase.  MiniMax Ent can be viewed as a generalization of MaxEnt for parametric linearinverse problems, and its complementarity with ML as yet another argument infavor of Shannon's entropy criterion.Comment: Presented at 'MaxEnt 2000', CNRS, Gif sur Yvette, France, July 8-13  200

MiniMax entropy and maximum likelihood: Complementarity of tasks, identity of solutions