A Modified Power Lindley Distribution

Many probability distributions have been discussed by various authors to model the lifetime data. However, looking into the variety of data coming in this era, there are more and more requirements for distributions to fit the data. This article introduces a new probability distribution, a modified power Lindley distribution, to fit a greater number of situations and more general applications. Its rich statistical properties are established. The proposed distribution can be used to model the data sets with decreasing, increasing, decreasing-increasing-decreasing and upside-down bathtub-shaped hazard rates. The parameters of the proposed distribution are estimated by the maximum likelihood method. A simulation study is carried out to compute the average estimate, bias, mean square error, and average width of the asymptotic confidence interval. Two real data sets are analyzed to illustrate the flexibility of the proposed model.