ABSTRACT
It was shown in .John (1961) arid Moml (1975) that the proha1)ilities of correct, classificatiorr can bc expressed in t,erms of t,he doubly nolrccr~trnl F'-distritmtioii if expectations :ire ~ d m o w r i Imt covariarrcc m;it,rices :ire known nnd eql~nl air(! the linear discrimirrar~t furictiori is ~lsed for classifying a.n intlivicl~lal iril,o onc of the populetions !Jl arid 112. It has been recently provixl. ill Krause i~iitl Itichte~ (1999), thiit the prohahilitics of correct classification can he also expressccl in terms of thc doubly i~onceritral E-dist~il~ution if both expectatioils and covariance rnatrices arc unknown but a ccrtttin gerlcralizet! rninirnurn-dist,ir.r~ce r ~ l c is uset1 for making the dccisioli. Here, a result, will be derived which is equivalent iri cori(,c.rit, to t,hc latt,cr on(: kmt different horn i t in forin. 'The rlretlrotl of proving this rcsult developed here difrers from that ill Krause arid llicht,cr (1999) in using basically a two-dirnensio~i;tl represcntaliori formula h.om the preceding scction whereas tllc proof of thc corresponding result in Krarlse and Richter (1999) starts frorri a. sample space r1rcasur.e represent at ion forni~ila.
