Classification into Two-Parameter Exponential Populations with a Common Guarantee Time

Abstract

SYNOPTIC ABSTRACTLet Π1, Π2, …, Πk be k (≥2) exponential populations with unknown scale parameters σ1, σ2, …, σk, respectively, and an unknown but common location parameter μ. First, we consider the estimation of scale parameters when an isotonic ordering among the scale parameters is present. We show the superiority of a class of mixed estimators over the maximum likelihood estimators of scale parameters under a scale-invariant loss function. Bayes and generalized Bayes estimates of scale parameters are obtained assuming proper and improper prior distributions, respectively. As an application of these new estimators, we have considered the problem of classifying an observation into one of k populations under order restrictions on scale parameters. Classification rules are proposed based on mixed estimators. We also derive plug-in Bayes classification rules and likelihood ratio-based classification rules. Extensive simulations are performed to compare these rules with respect to the expected probability of correct classification. An application of the classification rules is done on a real data set.