Lindley–Exponential distribution: properties and applications

In this paper, we introduce a new class of distributions generated by an integral transform of the probability density function of the Lindley distribution which results in a model that is more flexible in the sense that the derived model spans distributions with increasing failure rate, decreasing failure rate and upside down bathtub shaped hazard rate functions for different choices of parametric values. For this new model, various distributional properties including limiting distribution of extreme order statistics are established. Maximum likelihood estimators and the marginal confidence intervals of the parameters are obtained. The applicability of the proposed distribution is shown through application to real data sets. Through application to two real datasets, it is demonstrated that the proposed model fits better as compared to some other competing models. Further, the model is shown to be useful for analysing stress–strength model.