# On Reliability Approach to Multiple Hypotheses Testing and Identification of Probability Distributions of Two Stochastically Coupled Objects

## Abstract

This paper is devoted to logarithmically asymptotically optimal hypotheses testing and identification for a model consisting of two stochastically related objects. It is supposed that L1 possible probability distributions are known for the first object and the second object is distributed according to one of L1 x L2 given conditional distributions depending on the distribution index and the current observed state of the first object. The matrix of interdependencies of all possible pairs of the error probability exponents in asymptotically optimal tests of distributions of both objects is studied. The identification of the distributions of two objects gives an answer to the question whether r1-th and r2-th distributions occurred, or not on the first and the second objects, correspondingly.

## References

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*Mathematical Problems of Computer Science*,

*33*, 95–101. Retrieved from http://mpcs.sci.am/index.php/mpcs/article/view/337

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