Estimation of a Discriminant Function from a Mixture of Two Burr Type III Distributions

Abstract

In this article, we propose the finite mixture of two Burr Type-III distributions (MTBIIID). First, we formulate the proposed model with some properties and prove the identifiability property. Next, we obtain the maximum likelihood estimates (MLEs) of the unknown parameters of MTBIIID under classified and unclassified observations. Also, we estimate the nonlinear discriminant function of the underlying model. In addition, we calculate the total probabilities of misclassification as well as the percentage bias. Further, we investigate the performance of the all results through series of the simulation experiments by the means of the relative efficiencies.

Keywords:

• Discriminant function
• EM Algorithm
• Finite mixtures
• Identifiability
• Maximum likelihood estimation
• Monte Carlo simulations

Mathematics Subject Classification:

• 62F10
• 62E15