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As a contribution to literature, my work is a study to investigate a new way of classifying populations under the exponential power assumption. This was with a view to formulating an exponential power discriminant function and investigating the limiting case in accordance with an existing model. The discriminant function of the exponential power distribution was formulated using the Bayes maximum likelihood theorem The scale, location and the shape parameters were obtained numerically with the aid of Newton method in Matlab and R packages was used to obtain the Linear Discriminant Analysis (LDA) and the Quadractic Discriminant Analysis (QDA) of the data when the covariance matrices are equal and unequal respectively. Likewise Lachenbruch holdout procedure was used to check the error rates,whether it was advisable using the exponential power model or the existing procedure. The study concluded that exponential power distribution was a good replacement for normal distribution because it generalises the normal distribution.