Estimating and Updating a Linear Discriminant Function from the Mixture of Two One-Parameter Lindley Distributions

In this paper, we introduce the mixture model of two one-parameterLindley distributions through the mathematical formula of theprobability density and cumulative distribution functions of theunderlying mixture model. Then, we find out the maximum-likelihoodestimates of the parameters of the mixture of two one-parameterLindley distributions by using two types of data namely; classifiedand unclassified samples. Next, we estimate the linear discriminantfunction of the underlying mixture model and calculate the totalprobabilities of misclassification as well as the percentage biasthrough a series of simulation experiments and some real data sets.Consequently, we study the problem of updating the discriminantfunction on the basis of data of unknown origin. We consider theupdating procedure for the linear discriminant function on the basisof two one-parameter Lindley distributions in situations when theadditional observations are mixed or classified. Finally, we studythe performance of the updating procedures through some simulationexperiments by means of the relative efficiencies.