D:\sbornik\...\TPEL.DVI Mathematical Problems of Computer Science 32, 56{64, 2009. On Reliability Appr oach to I denti¯cation of P r obabilty Distr ibutions of T wo Statistically Dependent Objects A r a m O. Y e s s a ya n Institute for Informatics and Automation Problems of NAS of RA evhar@ipia.sci.am Abstract The identi¯cation of the distributions of two objects is an answer to the question whether r1-th and r2-th distributions occured, or not on the ¯rst and the second objects, correspondigly . Haroutunian and Hakobyan solved the problem reliable identi¯cation of probability distributions for two independent objects. In this paper we present the solution of the problem of logarithmically asymptotically optimal identi¯cation of probability distributions for two statistically dependent objects. Refer ences [1 ] E . A . H a r o u t u n ia n , \ L o g a r it h m ic a lly a s ym p t o t ic a lly o p t im a l t e s t in g o f m u lt ip le s t a t is t i- c a l h yp o t h e s e s " , P roblems of Control and Information Theory, vo l. 1 9 ( 5 -6 ) , p p . 4 1 3 { 4 2 1 , 1 9 9 0 . [2 ] R . F. A h ls we d e a n d E . A . H a r o u t u n ia n , \ On lo g a r it h m ic a lly a s ym p t o t ic a lly o p t im a l t e s t in g o f h yp o t h e s e s a n d id e n t ī c a t io n " . L e c t u r e N o t e s in Co m p u t e r S c ie n c e , vo l. 4 1 2 3 , \ Ge n e r a l Th e o r y o f In fo r m a t io n Tr a n s fe r a n d Co m b in a t o r ic s " , S p r in g e r , p p . 4 6 2 { 4 7 8 , 2 0 0 6 . [3 ] E . A . H a r o u t u n ia n , \ R e lia b ilit y in m u lt ip le h yp o t h e s e s t e s t in g a n d id e n t ī c a t io n " . P r o - c e e d in g s o f t h e N A TO A S I, Y e r e va n 2 0 0 3 , N A TO S c ie n c e S e r ie s , III: Co m p u t e r a n d S ys t e m s S c ie n c e s , vo l. 1 9 8 , IOS P r e s s , p p . 1 8 9 { 2 0 1 , 2 0 0 5 . [4 ] E . A . H a r o u t u n ia n a n d P . M. H a ko b ya n , \ On L A O t e s t in g o f m u lt ip le h yp o t h e s e s fo r p a ir o f o b je c t s " , M athematical P roblems of Computer Science, vo l. X X V , p p . 9 2 { 1 0 0 , 2 0 0 6 . [5 ] E . A . H a r o u t u n ia n a n d P . M. H a ko b ya n , \ On id e n t i¯ c a t io n o f d is t r ib u t io n s o f t wo in d e p e n d e n t o b je c t s " , M athematical P roblems of Computer Science, vo l. X X V III, p p . 1 1 4 { 1 1 9 , 2 0 0 7 . 5 6 A. Yessayan 5 7 [6 ] E . A . H a r o u t u n ia n a n d A . O. Y e s s a ya n , \ On h yp o t h e s e s t e s t in g fo r t wo d i®e r e n t ly d is t r ib u t e d o b je c t s " . M athematical P roblems of Computer Science, vo l. X X V I, p p . 9 1 { 9 6 , 2 0 0 6 . [7 ] E . A . H a r o u t u n ia n a n d A . O. Y e s s a ya n , \ On lo g a r it h m ic a lly a s ym p t o t ic a lly o p t im a l h yp o t h e s is t e s t in g fo r p a ir o f s t a t is t ic a lly d e p e n d e n t o b je c t s " , M athematical P roblems of Computer Science, vo l. X X IX , p p . 9 7 { 1 0 3 , 2 0 0 7 . [8 ] E . A . H a r o u t u n ia n a n d A . O. Y e s s a ya n , \ On o p t im a l h yp o t h e s is t e s t in g fo r p a ir o f s t o c h a s t ic a lly d e p e n d e n t o b je c t s " , M athematical P roblems of Computer Science, vo l. X X X I, p p . 4 9 { 5 9 , 2 0 0 8 . [9 ] E . A . H a r o u t u n ia n , M. E . H a r o u t u n ia n , a n d A . N . H a r u t yu n ya n , \ R e lia b ilit y c r it e r ia in in fo r m a t io n t h e o r y a n d in s t a t is t ic a l h yp o t h e s e s t e s t in g " , F oundations and Trends in Communications and Information Theory, vo l. 4 , n o . 2 -3 , 2 0 0 8 . ìÇ׳ϳ·ñáñ»Ý ϳËÛ³É ûµÛ»ÏïÝ»ñÇ Ñ³í³Ý³Ï³Ý³ÛÇÝ µ³ßËáõÙÝ»ñÇ ÝáõÛݳϳݳóÙ³Ý Ñáõë³ÉÇáõÃÛ³Ý Ùáï»óÙ³Ý Ù³ëÇÝ ². ºë³Û³Ý ²Ù÷á÷áõÙ Ðá¹í³ÍáõÙ ëï³óí³Í ¿ »ñÏáõ íÇ׳ϳ·ñáñ»Ý ϳËÛ³É ûµÛ»ÏïÝ»ñÇ Ñ³í³Ý³Ï³Ý³ÛÇÝ µ³ßËáõÙÝ»ñÇ ³ëÇÙåïáïáñ»Ý ûåïÇÙ³É ÝáõÛݳϳݳóÙ³Ý ËݹñÇ ÉáõÍáõÙÁ: ºñÏáõ ³ÝÏ³Ë ûµÛ»ÏïÝ»ñÇ ¹»åùáõÙ ËݹÇñÁ ÉáõÍí»É ¿ñ [5]-áõÙ: