The efficiency of a nonlinear discriminant function based on unclassified initial samples from a mixture of two Burr type XII populations

A nonlinear discriminant rule may be estimated by maximum likelihood estimation using unclassified observations. The performance of a nonlinear discriminant function based on a sample from a mixture of two Burr type XII distributions, with parameters c, k1, k2 and p, is examined. Asymptotic expansion and asymptotic expected values of probabilities of misclassification are presented. The asymptotic relative efficiencies (ARE) of mixture and classified discrimination procedures are evaluated and discussed for selected parameters. Computations show that for fixed c and p, as ℝ=ℝk1-k2ℝ increases the ARE increases. Also, for fixed c and ℝ, as p varies from 0.1 to 0.5 the values of ARE increases. On the other hand, for fixed p and ℝ, as c increases the ARE decreases.