Estimation and Classification Using Samples from Two Logistic Populations with a Common Scale Parameter

Abstract

AbstractThis paper deals with the estimation and classification of two logistic populations with a common scale and different location parameters. Utilizing the Metropolis–Hastings method, we compute the Bayes estimators of the associated unknown parameters. For this purpose, we consider gamma priors for the common scale parameter and normal priors for two location parameters. These Bayes estimators are compared with some of the existing estimators in terms of their bias and the mean squared error numerically. Moreover, utilizing these estimators for the associated parameters, we construct some classification rules in order to classify a single observation into one of the two logistic populations under the same model. The performances of each of the classification rules are evaluated through expected probability of misclassification, numerically. Finally, two real-life data sets have been considered in order to show the potential application of the model problem.KeywordsBayes estimatorClassification rulesExpected probability of misclassificationMetropolis–Hastings procedureNumerical comparison