Abstract
In this paper, a new flexible lifetime distribution is introduced by compounding the power Lindley and geometric distributions, called power Lindley geometric distribution (PLG). The proposed model can be used for business lifetime analysis such as investments failure, waiting time for services, delivery time, etc. This new distribution is an extension of Lindley geometric distribution [23]. Several of its properties, such as density, survival function, failure rate function, survival function, limiting behavior, quantile function, moments, and distribution of order statistics are studied. The method of maximum likelihood estimation (mle) will be used to estimate the model parameters of this new distribution. Asymptotic properties of the mle and simulation are introduced to address the performance of parameters estimate. At the end, we will apply the model on real data to show the flexibility and potential of the new distribution.