Mergel' V. Statistical estimation of entropy and its application in testing of statistical hypotheses

The dissertation work is a scientific research of properties of a statistical estimator of entropy constructed using the generalized spacing method, the last is used for construction of tests of goodness of fit for some probability distributions and for construction of test of independence. In this research the number of different problems have been studied and there were studied the conditions density function should satisfy to result such an estimators to be asymptotically unbiased and consistent, -consistent, and also there were found the conditions at which the order of a deviation of these estimators from exact meaning of entropy of probabilistic distribution at large N behaves as O(1/N). Besides it was formulated and proved the maximum entropy principle for some probabilistic distributions and it was offered to use these estimators for construction of test of independence.