D:\sbornik\...\IDENT2.DVI


Mathematical Problems of Computer Science 24, 2005, 76{81.

On Logar ithmically Asymptotically Optimal

H ypothesis T esting of T hr ee Distr ibutions for P air of

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

Institute for Informatics and Automation Problems of NAS of RA

e-mail evhar@ipia.sci.am, par h@ipia.sci.am

Abstract

The problem of hypotheses testing for a model consisting from two independent
objects is considered. It is supposed that three probability distributions are known and
objects independently from each other follow to one of them. The matrix of asymptotic
interdependencies (reliability{reliability functions) of all possible pairs of the error
probability exponents (reliabilities) in optimal testing for this model is studied.

The case with two independent objects and two given probability distributions was
elaborated by Haroutunian and Ahlswede.

Refer ences

[1 ] H a r o u t u n ia n E . A . " 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 ] A h ls we d e R . a n d W e g e n e r I., S e a r c h p r o b le m s . W ile y, N e w Y o r k, 1 9 8 7 .

[3 ] A h ls we d e R . F. a n d H a r o u t u n ia n E . A ." On S t a t is t ic a l H yp o t h e s e s Op t im a l Te s t in g a n d
Id e n t i¯ c a t io n " . M athematical P roblems of Computer Science 24, p p .1 6 { 3 3 , 2 0 0 5 .

[4 ] Co ve r T. M. a n d Th o m a s J. A . " E le m e n t s o f In fo r m a t io n Th e o r y" . W iley, New York,
1 9 9 1 .

[5 ] I. Cs is z ¶a r , " Th e m e t h o d o f t yp e s " , IE E E Trans. Inform. Theory, vo l. 4 4 , n o . 6 ,
p p . 2 5 0 5 { 2 5 2 3 , 1 9 9 8 .

[6 ] I. Cs is z ¶a r a n d J. K Äo r n e r , Information Theory: Coding Theorems for D iscrete M emo-
ryless Systems, A c a d e m ic P r e s s , N e w Y o r k, 1 9 8 1 , R u s s ia n t r a n s la t io n , Mir , Mu s c o w,
1 9 8 5 .

7 6



E. A. Haroutunian and P. M. Hakobyan 7 7

ºñÏáõ ³ÝÏ³Ë ûµÛ»ÏïÝ»ñÇ ½áõÛ·Ç Ýϳïٳٵ »ñ»ù í³ñϳÍÝ»ñÇ
Éá·³ñÃÙáñ»Ý ³ëÇÙåïáïáñ»Ý ûåïÇÙ³É ëïáõ·áõÙ

º. ². гñáõÃÛáõÝÛ³Ý ¨ ö. Ø. гÏáµÛ³Ý

²Ù÷á÷áõÙ

¸Çï³ñÏí³Í »Ý »ñÏáõ ³ÝÏ³Ë ûµÛ»ÏïÝ»ñÇó ϳ½Ùí³Í Ùá¹»ÉÇ Ñ³Ù³ñ í³ñϳÍÝ»ñÇ
ëïáõ·Ù³Ý ËݹÇñÁ: гÛïÝÇ »Ý »ñ»ù ѳí³Ý³Ï³Ý³ÛÇÝ µ³ßËáõٻݻñ, ¨ ûµÛ»ÏïÝ»ñÇó
Ûáõñ³ù³ÝãÛáõñÁ ³ÝϳËáñ»Ý ÁݹáõÝáõÙ ¿ ¹ñ³ÝóÇó Ù»ÏÁ: ²Ûë Ùá¹»ÉÇ Ñ³Ù³ñ
áõëáõÙݳëñÇí»É ¿ ûåïÇÙ³É ï»ëï³íáñÙ³Ý ³ñ¹ÛáõÝùáõÙ µáÉáñ Ñݳñ³íáñ ½áõÛ·»ñÇ
ë˳ÉÝ»ñÇ Ñ³í³Ý³Ï³ÝáõÃÛáõÝÝ»ñÇ óáõóÇãÝ»ñÇ (Ñáõë³ÉÇáõÃÛáõÝÝ»ñÇ) ÷áËϳËí³ÍáõÃ-
ÛáõÝÁ: ºñÏáõ ѳí³Ý³Ï³Ý³ÛÇÝ µ³ßËáõÙÝ»ñáí ¹»åùÁ áõëáõÙݳëÇñí»É ¿ гñáõÃÛáõÝÛ³ÝÇ
¨ ²Éëí»¹»Ç ÏáÕÙÇó [3]: