ArticleArsen0728F.DVI Mathematical Problems of Computer Science 23, 2004, 67{79. T wo-dimensional Sequence H omogeneity T esting Against M ixtur e Alter native¤ Ir in a A . S a fa r ya n , E vg u e n i A . H a r o u t u n ia n a n d A r s e n V . Ma n a s ya n Institue for Informatics and Automation Problems of NAS of RA e-mail evhar@ipia.sci.am Abstract The behavior of linear rank statistics is investigated on models in which various subsequences of observations follow di®erent statistical distributions. Such data can be interpreted both as models of a ¯nite number distribution mixtures and as dependence models. We apply data set simulation to obtain estimates of average and variance of used rank statistics. The modeled and asymptotic results are enough close. Refer ences [1 ] L a u s e n B ., S h u m a c h e r H ., " Ma xim a lly s e le c t e d r a n k s t a t is t ic s " , B io m e t r ic s , 4 8 , p p . 7 3 -8 5 , 1 9 9 2 . [2 ] H a r o u t u n ia n E ., S a fa r ya n I. " D is t r ib u t io n s m ixt u r e d ivis io n wit h a s t r a t ifyin g p a r a m e - t e r " , s u b m it t e d fo r p u b lic a t io n . [3 ] S a fa r ya n I., H a r o u t u n ia n E . " A Co m m o n a p p r o a c h t o t h e d is t r ib u t io n s m ixt u r e id e n t i- ¯ c a t io n a n d d e p e n d e n c e m o d e ls a n a lys is " , P r o c e e d in g s o f CSIT 2003, p p . 1 8 4 -1 8 6 . [4 ] H a r o u t u n ia n E . a n d S a fa r ya n I. " N o n p a r a m e t r ic c o n s is t e n t e s t im a t io n o f t h e c h a n g e m o m e n t o f r a n d o m s e qu e n c e p r o p e r t ie s " , Transactions of Institute for Informatics and Automation P roblems of NAS of R A and of YSU, M athematical P roblems of Computer Science, vo l. 1 7 , p p . 7 6 -8 5 , 1 9 9 7 . [5 ] H o t h o r n T., 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 . ¤The work was partially supported by INTAS, project 00-738. 6 7 6 8 Two-dimensional Sequence Homogeneity Testing Against Mixture Alternative ʳéÝáõñ¹Ç »ñÏÁÝïñ³ÝùÇ Ñ³Ý¹»å »ñÏã³÷³ÝÇ Ñ³çáñ¹³Ï³ÝáõÃÛ³Ý Ñ³Ù³ë»éáõÃÛ³Ý ëïáõ·áõÙÁ º. гñáõÃÛáõÝÛ³Ý, Æ. ê³ý³ñÛ³Ý ¨ ². سݳëÛ³Ý ²Ù÷á÷áõ٠лﳽáïí³Í ¿ ·Í³ÛÇÝ Ï³ñ·³ÛÇÝ íÇ׳ϳÝÇÝ»ñÇ í³ñùÁ Ùá¹»ÉÝ»ñáõÙ, áñï»Õ ¹Çï³ñÏáõÙÝ»ñÇ Ñ³çáñ¹³Ï³ÝáõÃÛáõÝÝ»ñÁ »ÝóñÏíáõÙ »Ý ï³ñµ»ñ íÇ׳ϳ·ñ³Ï³Ý µ³ßËáõÙÝ»ñÇ: ²Û¹åÇëÇ ïíÛ³ÉÝ»ñÁ ϳñ»ÉÇ ¿ Ù»Ïݳµ³Ý»É ¨ áñå»ë í»ñç³íáñ Ãíáí µ³ßËáõÙÝ»ñÇ Ë³éÝáõñ¹ Ùá¹»ÉÝ»ñ, ¨ áñå»ë ϳËí³ÍáõÃÛ³Ý Ùá¹»ÉÝ»ñ: Ø»Ýù ÏÇñ³éáõÙ »Ýù ïíÛ³ÉÝ»ñÇ µ³½ÙáõÃÛ³Ý ÙṻɳíáñáõÙª û·ï³·áñÍí³Í ϳñ·³ÛÇÝ íÇ׳ϳÝÇÝ»ñÇ ÙÇçÇÝÝ»ñÇ ¨ óñí³ÍùÝ»ñÇ ·Ý³Ñ³ï³Ï³ÝÝ»ñÇ ëï³óÙ³Ý Ñ³Ù³ñ: ØṻɳíáñÙ³Ý ¨ ³ëÇÙåïáï³Ï³Ý ³ñ¹ÛáõÝùÝ»ñÁ µ³í³Ï³Ý³ã³÷ Ùáï »Ý: