D:\sbornik\...\Untitled1.DVI Mathematical Problems of Computer Science 26, 2006, 91{96. On H ypothesis Optimal T esting for T wo Di®er ently Distr ibuted Objects E vg u e n i A . H a r o u t u n ia n a n d A r a m O. Y e s s a ya n Institue for Informatics and Automation Problems of NAS of RA e-mail evhar@ipia.sci.am Abstract Hypotheses identi¯cation for two objects having di®erent distributions from two given probability distrubutions was examined by R. Ahlswede and E. Haroutunian. We investigate a model with two objects having di®erent distributions from three possible distributions. The matrix of all possible pairs of asymptotical interdependencies of the realabilities (error probability exponents) for logarithmically asymptotically optimal testing is studied. Refer ences [1 ] E . 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 ic 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 . A h ls we d e a n d I. W e g e n e r " S e a r c h p r o b le m s " . W ile y, N e w yo r k, 1 9 8 7 . [3 ] E . 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 i¯ c a t io n " . 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 -V o l 1 9 8 , p p . 1 8 9 -2 0 1 . 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 , 2 0 0 5 IOS P r e s s . [4 ] E . H a r o u t u n ia n a n d P . H a ko b ya n " On lo g a r it h m ic a lly o p t im a l h yp o t h e s is t e s t in g o f t h r e e d is t r ib u t io n s fo r p a ir o f in d e p e n d e n t o b je c t s " , M athematical P roblems of Com- puter Sciences, vo l. X X IV , Y e r e va n 2 0 0 5 , p p . 7 6 -8 1 . [5 ] I. Cs is z ¶a r a n d P . C. S h ie ld s " In fo r m a t io n t h e o r y a n d s t a t is t ic s : a t u t o r ia l" . F oundations and Trends in Communications and Information Theory. V o lu m e 1 , Is s u e 4 , 2 0 0 4 . [6 ] T. M. Co ve r a n d J. A . Th o m a s " E le m e n t s o f in fo r m a t io n t h e o r y" . W ile y, N e w Y o r k, 1 9 9 1 . [7 ] R . E . B e c h h o fe r , J. K ie fe r a n d M. S o b e l " S e qu e n t ia l id e n t i¯ c a t io n a n d r a n kin g p r o c e d u r e s " , Th e U n ive r s it y o f Ch ic a g o , 1 9 6 8 . 9 1 9 2 On Optimal Testing of Three Hypotheses for Two Dependent Objects î³ñµ»ñ µ³ßËáõÙÝ»ñáí »ñÏáõ ûµÛ»ÏïÝ»ñÇ Ýϳïٳٵ »ñ»ù í³ñϳÍÝ»ñÇ ûåïÇÙ³É ëïáõ·Ù³Ý Ù³ëÇÝ º. гñáõÃÛáõÝÛ³Ý ¨ ². ºë³Û³Ý ²Ù÷á÷áõÙ ¸Çï³ñÏí³Í ¿ »ñÏáõ ϳËÛ³É ûµÛ»ÏïÝ»ñÇó ϳ½Ùí³Í Ùá¹»ÉÇ Ñ³Ù³ñ »ñ»ù í³ñϳÍÝ»ñÇ ëïáõ·Ù³Ý ËݹÇñÁ: ºñ»ù ѳí³Ý³Ï³Ý³ÛÇÝ µ³ßËáõÙÝ»ñÁ ѳÛïÝÇ »Ý, ¨ ûµÛ»ÏïÝ»ñÁ ÁݹáõÝáõÙ »Ý ÙÇÙÛ³Ýó ãÏñÏÝáÕ µ³ßËáõÙÝ»ñ ïñí³ÍÝ»ñÇó: ²Ûë Ùá¹»ÉÇ Ñ³Ù³ñ áõëáõÙݳëÇñí»É ¿ ûåïÇÙ³É ï»ëï³íáñÙ³Ý ¹»åùáõÙ µáÉáñ Ñݳñ³íáñ ½áõÛ·»ñÇ ë˳ÉÝ»ñÇ Ñ³í³Ý³Ï³ÝáõÃÛáõÝÝ»ñÇ óáõóÇãÝ»ñÇ (Ñáõë³ÉÇáõÃÛáõÝ»ñÇ) ÷áËϳËí³ÍáõÃÛáõÝÁ: