This paper describes a threshold classification with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$K$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>K</mi> </math> </EquationSource> </InlineEquation> populations whose membership category is associated with the threshold process of a latent variable. It is seen that the optimal procedure (Bayes procedure) for the classification involves a nonlinear classification rule and...</equationsource></equationsource></inlineequation>