ABSTRACT
Let an individual having a Gaussian distributed feature variable belong to one of two distinct populations. Assume that we are given measurements from a sarnplc of individuals giving rise to indcpcridcnt and identically distributed Gaussian feature variables. Several rnethods of allocating the individual or the whole sample to one of the two populat ion~ have been studied in the literature. For an introduction to this area see, e.g., Anderson (1984) or McLachlan (1992). A certa,in subclass of classificatiori rules is given by the so-called distance rules. Becausc of the great variety of distances existing in statistics, there arc several approaches to distance based classification rules, as only to mcntion Cacoullos and Koutras (1985), Cacoullos (19921, and Cacoullos and Koutras (1996). When choosing a method for classifying an individual or a sample of individuals, one has to distinguish between the cases of known or uriknown rnornerits. Certain sarnplc-distance based classification rules, however, work without assurriptions concerning the second
order rrlorrlcrrts and prohtbilit,ies of correct classification can be desa.ibctl explicitly ill tcrrns of thrw morr~ents. This advantage hits been exploited to sonic extent recently in I<r;tuse a,nd Richter (1999). 'l'hc mctllod dcvelopcd there conlbines a geometric sample measure representation forrrllrla for the ~nultivariate Gij,ussia.r~ rneasure with a ccrttiirl non classic lirlear model aplxoacll due to Krause and Richter (1994). 7'11% linear motlcl type approach will bc rnotlified in the present paper to derive iiew represcntai,ion forrrrulae for prol)abilit,ics of correct classification which arc based npon the two-dir~letlsional Ga~lssi;r.n lmr. Further transforrrlntion of these f'orrnulae yields expressions ill t,crrris of the doubly noncc1ltra.l b-distributioi~ as has lwen clcrived rccc~~t ly in another way in Eimlsc: and Richter ( 1999).
