The Exponentiated Poisson-Lindley Distribution; Features and Applications in Reliability

Abstract. In this paper a new three-parameter lifetime distribution named “the Exponentialed Lindley-Poisson (E-LP) distribution” has been suggested that it has an  increasing, decreasing and invers bathtube hazard rate depending on the parameter values. The (E-LP) distribution has applications in economics, actuarial modeling, reliability modeling, lifetime and queuing problems and biological sciences. Firstly, the mathematical and statistical characteristics of the proposed distribution are presented, then the applications of the new distribution are studied using the real data set. expressions for moments, skewness and kurtosis have been given. Various mathematical and statistical properties of the proposed distribution have been discussed. Estimation of its parameter has been discussed using the method of maximum likelihood. A simulation study is given. In the end, two applications of the new distribution have been discussed with two real lifetime data sets. The results also confirmed the suitability of the presented models for real data collection.