Small sample results for a nonlinear discriminant function estimated from a mixture of two burr type XII distributions

Abstract

The problem of identifiability of finite mixture of Burr type XII distributions is studied. A procedure is presented for finding maximum likelihood estimates of the parameters of a mixture of two Burr type XII distributions, using classified and unclassified observations. Estimation of a nonlinear discriminant function on the basis of a small sample size is considered. Its performance is investigated by a series of simulation experiments. The simulations conducted for estimating a nonlinear discriminant function by maximum likelihood, on the basis of unclassified data drawn from a mixture of the underlying populations suggest that the error rate can be reduced by a substantial percentage for widely separated populations. Generally, the performance of the mixture discrimination procedure relative to the completely classified procedure, measured by total probabilities is good.