D:\sbornik\...\article_eng.DVI Mathematical Problems of Computer Science 31, 40{48, 2008. Copulas of T wo-Dimensional T hr eshold M odels E vg u e n i A . H a r o u t u n ia n a n d Ir in a A . S a fa r ya n Institute for Informatics and Automation Problems of NAS of RA. E-mail: evhar@ipia.sci.am Abstract A representation of two-dimensional random vector bivariate distribution by copula is proposed for the case when one of components is categorizing for the other. The regression function and the bounds for the Spearman rank correlation coe±cient are derived. Refer ences [1 ] H . Jo e , \ Mu lt iva r ia t e m o d e ls a n d d e p e n d e n c e c o n c e p t s " , Chapman and Hall, L ondon, 1 9 9 7 . [2 ] B . S c h we iz e r a n d E . F. W o l®, \ On n o n p a r a m e t r ic m e a s u r e s o f d e p e n d e n c e fo r r a n d o m va r ia b le " , The Annals of Stat., vo l. 9 , n u m . 6 , p p . 8 7 9 { 8 8 6 , 1 9 8 1 . [3 ] P . E m b r e c h t s , A . Mc N e il a n d D . S t r a u m a n , \ Co r r e la t io n a n d d e p e n d e n c e in r is k m a n - a g m e n t . P r o p e r t ie s a n d p it fa lls " , In: R isk M anagement: Value at R isk and B eyond (M D empster E d.) Cambridge University P ress,, p p . 1 7 6 { 2 2 3 , 2 0 0 2 . [4 ] B . L a u s e n a n d M. S h u m a c h e r , \ Ma xim a l s e le c t e d r a n k s t a t is t ic s " , B iometrics, vo l. 4 8 , p p . 7 2 { 8 5 , 1 9 9 2 . [5 ] H o t h o r n T. a n d L a u s e n B ., " On t h e e xa c t d is t r ib u t io n o f m a xim a lly s e le c t e d r a n k s t a t is - t ic s " , Comp. Statist. and D ata Anal., vo l. 4 3 , p p . 1 2 1 - 1 3 7 , 2 0 0 3 . [6 ] S a fa r ya n I., H a r o u t u n ia n E . a n d Ma n a s ya n A ., \ Two -d im e n t s io n a l s e qu e n c e h o m o g e n e it y t e s t in g a g a in s t m ixt u r e a lt e r n a t ive " , M athematical problems of computer science, vo l. 2 3 , p p . 6 7 { 7 9 , 2 0 0 4 . ºñÏã³÷ ß»Ùù³ÛÇÝ Ùá¹»ÉÝ»ñÇ Ï³å³ÏóÇãÁ º. гñáõÃÛáõÝÛ³Ý ¨ Æ. ê³ý³ñÛ³Ý ²Ù÷á÷áõÙ ²é³ç³ñÏí³Í ¿ »ñÏã³÷ å³ï³Ñ³Ï³Ý í»ÏïáñÇ µ³ßËÙ³Ý ýáõÝÏódzÛÇ Ï³å³ÏóÇãÇ (copula) ÙÇçáóáí Ý»ñϳ۳óáõÙÁ ³ÛÝ ¹»åùÇ Ñ³Ù³ñ »ñµ í»ÏïáñÇ µ³Õ³¹ñÇãÝ»ñÇó Ù»ÏÁ ½³ïáÕ ¿ ÙÛáõëÇ Ñ³Ù³ñ: êï³óí³Í »Ý é»·ñ»ëÇáÝ ýáõÝÏóÇ³Ý ¨ êåÇñÙ»ÝÇ Ï³ñ·³ÛÇÝ Ñ³ñ³µ»ñ³ÏóáõÃÛ³Ý ·áñͳÏóÇ í»ñÇÝ ¨ Ý»ñùÇÝ ·Ý³Ñ³ï³Ï³ÝÝ»ñÁ: 4 0