A Note on Different Types of Probabilities of Misclassification

Whenever a discriminant function is constructed, the attention of a researcher is often focused on classification. The underlined interest is how well does a discriminant function perform in classifying future observations correctly. In order to assess the performance of any classification rule, probabilities of misclassification of a discriminant function serves as a basis for the procedure. Different forms of probabilities of misclassification and their associated properties were considered in this study. The misclassification probabilities were defined in terms of probability density functions (pdf) and classification regions. Apparent probability of misclassification is expressed as the proportion of observations in the initial sample which are misclassified by the sample discriminant function. Different methods of estimating probabilities of misclassification were related to each other using their individual shortcomings. The status of degrees of uncertainties associated with probabilities of misclassification and their implications were also specified.