The mathematical models development. The usage of the information theory methods under the approximation of the multi-measures densities distributions of observations

Abstract

Under the decisions of the huge quantity of problems in the different scientifical and technical branchs the used signals are described by models, which must be adequate to real signals. The well-known models are based on the Gauss random processes. However in the real information systems the signals have non-gaussian character and they have to be described by the non-gaussian distributions of momentary values. In this work it is given the analysis of the wide-spread information quantity measures, introduced by Fisher, Shennon, Kulback and Liebrer. Under the mathematical hypothesises verification the similarity criterion was used as the most informative. The Kulback results have the limitations and shortcomings, consist in the single-measure quantities usage and the non-evident presentation of the searched density distribution, what produces the difficulties under these results analysis and usage. The work includes the investigations, carried out on the base of the Lagrange factors methods and eliminate by some degree the above mentioned limitations and shortcomings. The known results for the single-measure distributions were generalized and thus the new results were obtained in relation to the multi-measure case.