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

This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. 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.