Two-Stage LAO Detection of Distribution for Arbitrarily Varying Object with the Pair of Families of Distributions

Multiple statistical hypotheses two-stage testing to make choice between hypotheses concerning distribution of discrete arbitrarily varying object is investigated. In the first stage one family of distributions is detected and then in the second stage, one distribution is denoted in mentioned family. The matrix of optimal asymptotic interdependencies of all pairs of the error probability exponents (reliabilities) are studied for arbitrarily varying object with the current states sequence known to the statistician. The goal of research is to express the optimal functional relations for all parts of reliabilities of LAO testing by two stages.