Ordered classification rules for inverse gaussian populations with unknown parameters
Nabakumar Jana, Somesh Kumar · Journal of Statistical Computation and Simulation · 2019
Let Π1,Π2,…,Πk be k (≥ 2) populations with Πi having an inverse Gaussian distribution with unknown mean μi and unknown scale-like parameter λi, 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 λis follow an ordering. When the means are unequal, we also derive rules assuming ordering among either λis or μis. 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.