Empirical comparison of the performance of linear discriminant function under multivariate non-normal and normal data

Abstract

Discriminant analysis is a multivariate technique concerned with classifying distinct set of objects (or set of observations) and with allocating new objects (or observations) to the previously defined groups. Fisher linear discriminant function is studied under multivariate normal as well as non-normal data. The different multivariate non-normal and normal populations are simulated by using distinct mean vectors and dispersion matrix for rice and maize data sets. Further fifty different independent samples each are simulated for different dimensions and sample sizes for maize and rice data to obtain empirical probabilities of misclassification in case of non-normal data. Taking into consideration the overall results of maize and rice, it has been noticed that D² values and discriminating power are higher in 58 per cent and 86 per cent cases, respectively irrespective of sample size and dimensions in case of normal data compared to non-normal data. The probabilities of misclassification are more in case of multivariate non-normal data compared to normal data.