Alternative classification rules for two inverse gaussian populations with a common mean and order restricted scale-like parameters

The problem of classification into two inverse Gaussian populations with a common mean and ordered scale-like parameters is considered. Surprisingly, the maximum likelihood estimators (MLEs) of the associated model parameters have not been utilized for classification purposes. Note that the MLEs of the model parameters, including the MLE of the common mean, do not have closed-form expressions. In this paper, several classification rules are proposed that use the MLEs and some plug-in type estimators under order restricted scale-like parameters. In the sequel, the risk values of all the proposed estimators are compared numerically, which shows that the proposed plug-in type restricted MLE performs better than others, including the Graybill-Deal type estimator of the common mean. Further, the proposed classification rules are compared in terms of the expected probability of correct classification (EPC) numerically. It is seen that some of our proposed rules have better performance than the existing ones in most of the parameter space. Two real-life examples are considered for application purposes.