D:\sbornik\...\IDENM2.DVI Mathematical Problems of Computer Science 28, 2007, 114{119. On I denti¯cation of Distr ibutions of T wo I ndependent Objects E vg u e n i A . H a r o u t u n ia n a n d P a r a n d z e m M. H a ko b ya n Institue for Informatics and Automation Problems of NAS of RA e-mail: evhar@ipia.sci.am Abstract Ahlswede and Haroutunian formulated new problems on multiple hypotheses testing and on identi¯cation of hypotheses. The problems of identi¯cation of distribution and of distributions ranking for one object were solved completely. In this paper we study the problem of identi¯cation of distributions for two independent objects. Refer ences [1 ] 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 i¯ c a t io n p r o b - le m s " . 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 , p p . 1 8 9 { 2 0 1 . IOS P r e s s , 2 0 0 5 . [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 ] R . E . B e c h h o fe r , J. K ie fe r , a n d M. S o b e l, Sequential identi¯cation and ranking proce- dures. Th e U n ive r s it y o f Ch ic a g o P r e s s , Ch ic a g o , 1 9 6 8 . [4 ] R . F. A h ls we d e a n d I. W e g e n e r , Search problems. W ile y, N e w Y o r k, 1 9 8 7 . [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 L A O t e s t in g o f m u lt ip le h yp o t h e s is fo r p a ir o f o b je c t s " , M athematical P roblems of Computer Science vol. 26, p p . 9 2 { 1 0 0 , 2 0 0 5 . [6 ] E . A . H a r o u t u n ia n a n d P . M. H a ko b ya n , \ On m u lt ip le h yp o t h e s e s L A O t e s t in g fo r m a n y in d e p e n d e n t o b je c t s " . ( A c c e p t t e d t o IE E E In t e r n a t io n a l S ym p o s iu m o n In fo r - m a t io n Th e o r y, Fr a n c e , N ic e , 2 0 0 7 ) . [7 ] 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 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 . [8 ] I. Cs is z ¶a r a n d J. K Äo r n e r , Information theory: coding theorems for discrete memoryless systems, A c a d e m ic P r e s s , N e w Y o r k, 1 9 8 1 . 1 1 4 E. A. Haroutunian and P. M. Hakobyan 1 1 5 ºñÏáõ ³ÝÏ³Ë ûµÛ»ÏïÝ»ñÇ µ³ßËáõÙÝ»ñÇ ÝáõÛݳϳݳóÙ³Ý Ù³ëÇÝ º. ². гñáõÃÛáõÝÛ³Ý ¨ ö. Ø. гÏáµÛ³Ý ²Ù÷á÷áõÙ ²Éëí»¹»Ý ¨ гñáõÃÛáõÝÛ³ÝÁ ÉáõÍ»É »Ý í³ñϳÍÝ»ñÇ ÝáõÛݳϳݳóÙ³Ý ËݹÇñÁ Ù»Ï ûµÛ»ÏïÇ ¹»åùáõÙ: ²Ûë Ñá¹í³ÍÁ ÝíÇñí³Í ¿ µ³ßËáõÙÝ»ñÇ ÝáõÛݳϳݳóÙ³Ý ËݹñÇ ÉáõÍÙ³ÝÁ »ñÏáõ ³ÝÏ³Ë ûµÛ»ÏïÝ»ñÇó ϳ½Ùí³Í Ùá¹»ÉÇ Ñ³Ù³ñ: