Discriminant analysis involving count data

Abstract

A situation giving rise to a violation of the normality assumption in discriminant analysis is that which involves count observations. For a two-variable case involving count observations, this paper presents a new discriminant analysis approach when one variable is observed conditional on the other. Two cases involving Poisson-Binomial and Poisson-Poisson distributions were considered. The derived allocation rules are based on the resulting joint distribution of the two count variables. Applicability of the suggested allocation rules in discriminant analysis involving count data and its performance in comparison with Fisher linear discriminant rule was studied under different conditions. Results obtained show promising applicability of the suggested allocation rules when compared with the Fisher linear discriminant method.

Keywords

• count data
• discriminant analysis
• error rate
• allocation rules
• poisson distribution
• binomial distribution