# On Logarithmically Asymptotically Optimal Hypothesis Testing of Distributions for Pair of Statistically Dependent Objects

## Abstract

The problem of hypotheses testing for a model consisting of two statistically dependent objects is considered. It is supposed that two probability distributions are known for the first object and the second object dependent on the first can be distributed according to one of two given conditional distributions. The matrix of asymptotical optimal interdependencies (reliability-reliability functions) of all possible pairs of the error probability exponents (reliabilities) is studied. The case with two objects which can't have the same probability distribution from two given was discussed by Ahlswede and Haroutunian and for three hypotheses by Haroutunian and Yessayan.

## References

E.A. Haroutunian, “Logarithmically asymptotically optimal testing of multiple statistical hypotheses", Problems of Control and Information Theory, vol. 19 (5-6), pp. 413-421, 1990.

R.F. Ahlswede and E.A. Haroutunian, “On logarithmically asymptotically optimal testing of hypotheses and identification". Lecture Notes in Computer Science, vol. 4123, “General Theory of Information Transfer and Combinatorics" Springer, pp. 462-478, 2006.

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E.A. Haroutunian and P.M. Hakobyan, “On logarithmically optimal hypothesis testing of three distributions for pair of independent objects", Mathematical Problems of Computer Sciences, vol. XXIV, Yerevan, pp. 76-81, 2005.

E.A. Haroutunian and P.M. Hakobyan, “On LAO testing of multiple hypotheses for pair of object", Mathematical Problems of computer Science, vol. XXV, Yerevan, pp. 93-101, 2006.

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E.A. Haroutunian and A.O. Yessayan, “On hypotheses testing for two differently distributed objects". Mathematical Problems of computer Science, vol. XXVI, Yerevan, pp. 91-96, 2006.

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*Mathematical Problems of Computer Science*,

*29*, 97–103. Retrieved from http://mpcs.sci.am/index.php/mpcs/article/view/452

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