Testing of Hypothesis and Identification

We introduce a new aspect of the influence of the information-theoretical methods on the statistical theory. The procedures of the probability distributions identification for K ( ≥ 1 ) random objects each having one from the known set of M ( ≥ 2 ) distributions are studied. N-sequences of discrete independent random variables represent results of N observations for each of K objects. On the base of these data decisions must be made concerning probability distributions of the objects. For N → ∞ the exponential decrease of the testʹs error probabilities is considered. The reliability matrices of logarithmically asymptotically optimal procedures are investigated for some models and formulations of the identification problem. The optimal subsets of reliabilities which values may be given beforehand and conditions guaranteeing positiveness of all the reliabilities are investigated.