Some new classification rules forcunivariate normal populations
Arjun K. Gupta, Zakkula Govindarajulu · Canadian Journal of Statistics · 1973
Abstract In this paper we propose classification rules with respect to the mean, variance, and the coefficient of variation forc(≥2)univariate normal populations. Two different approaches to the problem have been studied (a) where the probability of correct classification is at least a pre‐assigned numberp*(l/c ≤ p* < 1), and(b)where the probability of correct classification has to be evaluated. For the two approaches(a)and(b), classification rules with respect to the mean have been studied when thecpopulations have(i)common known variance,(ii)common unknown variance. The classification rules of approach(b)in the case of common known or unknown variance is also valid when the variances are not all equal and are known or unknown. Classification rules with respect to the coefficient of variation are also given for the two approaches when the population parameters are unknown. Classification rules with respect to the variance for the two approaches are explored when the means are unknown. In each case of approach(b), the classification rule has been shown to possess a certain optimum property.