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Estimation of a Discriminant Function Based on Small Sample Size from a Mixture of Two Gumbel Distributions

The identifiability of finite mixture of Gumbel distributions is proved. A procedure is presented for finding maximum likelihood estimates for the four parameters of a mixture of two Gumbel distributions, using classified and unclassified observations. A nonlinear discriminant function for a mixture of two Gumbel distributions is derived and estimated based on small sample size. Throughout simulation experiments, the performance of the corresponding estimated nonlinear discriminant function is investigated.