The present paper addresses a mixture of one-parameter Lindley and Weibull distributions from both practical and theoretical points of view. On the other hand, the aim of this paper is to set the record straight about this mixture. First, we introduce the mixture of one-parameter Lindley and Weibull distributions. Consequently, we study the main statistical properties of the proposed mixture model with some graphs of both density and hazard rate functions. Next, we estimate the unknown parameters of the mixture of one-parameter Lindley and Weibull distributions via the generalized method of moments and the maximum likelihood method. However, the bias, mean squared error and the relative efficiency of the estimated parameters are calculated using a Monte Carlo simulation study. The coverage probability and average width of the estimated intervals are also computed to examine the quality of the estimation methods. Finally, we evaluate the performance of our results with some simulation experiments and real data applications.
Digital Object Identifier (DOI)
F. Daghestani, A.; S. Sultan, K.; and Al-Moisheer, S.
"Mixture of Lindley and Weibull Distributions: Properties and Estimation,"
Journal of Statistics Applications & Probability: Vol. 10
, Article 3.
Available at: https://dc.naturalspublishing.com/jsap/vol10/iss2/3