Mixture of Lindley and Lognormal Distributions: Properties, Estimation, and Application

Finite mixture models provide a flexible tool for handling heterogeneous data. This paperintroduces a new mixture model which is the mixture of Lindley and lognormal distributions(MLLND). First, the model is formulated, and some of its statistical properties arestudied. Next, maximum likelihood estimation of the parameters of the model is considered,and the performance of the estimators of the parameters of the proposed models isevaluated via simulation. Also, the flexibility of the proposed mixture distribution isdemonstrated by showing its superiority to fit a well-known real data set of 128 bladdercancer patients compared to several mixture and nonmixture distributions. The KolmogorovSmirnov test and some information criteria are used to compare the fitted models to thereal dataset. Finally, the results are verified using several graphical methods.