A minmax problem statement of a problem of the parameter identification of the input/output mapping of systems is considered, based on the entropy (in the Shannon sense) of the identification error. Using the entropy based approach, a Gauss closeness measure is proposed, that simultaneously may serve as a simple test for the normality for any continuous probability distribution, suitable for applications within depended observations. A case study is considered, with confirming the full practical suitability of the theoretical considerations of the paper.