Mixture of Two One-Parameter Lindley Distributions: Properties and Estimation

In this paper, we discuss a mixture of two one-parameter Lindley distributions from both practical and theoretical point of view. The aim of this paper is to set the record straight about this mixture model from different sides. First, we present a brief summary of the Lindley distribution with one parameter. Then, we display the probability density and cumulative distribution functions of the mixture model of two one-parameter Lindley distributions. Consequently, we study some statistical properties of the mixture model with some graphs of both density and hazard rate functions. Also, we focus on the identifiable property of the mixture model and prove it. In addition, we estimate the unknown parameters of the mixture model via suitable methods such as the maximum likelihood and the generalized method of moments. However, we estimate the confidence intervals of the estimated parameters and compute the coverage probability and the average length of the estimated intervals. Finally, we evaluate the performance of our results through a simulation study, numerical examples and real data applications.