Three Probabilities of Misclassification

Abstract

The “probability of misclassification” is a natural criterion for evaluating a classification procedure, but this probability can be defined in various ways. Confusion can arise if the various definitions are not distinguished, on the other hand some of the definitions may lead to probabilities so close in numerical value that the distinction is of no practical importance. Here in the context of normal populations and a commonly used classification rule, the relationship between three probabilities of misclassification is examined, and the necessity and possibility of estimating them separately is considered.