Ordered classification rules for inverse gaussian populations with unknown parameters. Issue 14 (22nd September 2019) - Jana, Nabakumar; Kumar, Somesh
ABSTRACT: Let Π 1, Π 2, …, Π k be k ( ≥ 2 ) populations with Π i having an inverse Gaussian distribution with unknown mean μ i and unknown scale-like parameter λ i, 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 λ i s follow an ordering. When the means are unequal, we also derive rules assuming ordering among either λ i s or μ i 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.