D:\sbornik\...\Aram_13\Aram.DVI


Mathematical Problems of Computer Science 33, 95{101, 2010.

On Reliability Appr oach to M ultiple H ypotheses

T esting and I denti¯cation of P r obability Distr ibutions

of T wo Stochastically Coupled Objects

E vg u e n i H a r o u t u n ia n a n d A r a m Y e s s a ya n

Institute for Informatics and Automation Problems of NAS of RA
evhar@ipia.sci.am

Abstract

This paper is devoted to logarithmically asymptotically optimal hypotheses testing
and identi¯cation for a model consisting of two stochastically related objects. It is
supposed that L1 possible probability distributions are known for the ¯rst object and
the second object is distributed according to one of L1 £ L2 given conditional distri-
butions depending on the distribution index and the current observed state of the ¯rst
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 identi¯cation of the distributions of two objects gives an answer to the question
whether r1-th and r2-th distributions occurred, or not on the ¯rst and the second
objects, correspondingly.

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