Ordered classification rules for inverse gaussian populations with unknown parameters

Abstract

ABSTRACTLet be populations with having an inverse Gaussian distribution with unknown mean and unknown scale-like parameter , respectively. We study the problem of classification of an observation when prior information suggests some orderings on parameters. When the means are equal but unknown, we derive plug-in Bayes classification rules based on the maximum likelihood estimator (MLE), Graybill-Deal type estimator and shrinkage estimator of the common mean. When all parameters are unknown and unequal, we also derive likelihood ratio-based classification rules. For more than two populations, we suggest ordered rules when s follow an ordering. When the means are unequal, we also derive rules assuming ordering among either s or s. Extensive simulations are carried out to compare the proposed rules with respect to expected probabilities of correct classification. Applications of these classification rules are described using real data sets.