Two Families of Continuous Probability Distributions Generated by the Discrete Lindley Distribution

Abstract

In this paper, we construct two new families of distributions generated by the discrete Lindley distribution. Some mathematical properties of the new families are derived. Some special distributions from these families can be constructed by choosing some baseline distributions, such as exponential, Pareto and standard logistic distributions. We study in detail the properties of the two models resulting from the exponential baseline, among others. These two models have different shape characteristics. The model parameters are estimated by maximum likelihood, and related algorithms are proposed for the computation of the estimates. The existence of the maximum-likelihood estimators is discussed. Two applications prove its usefulness in real data fitting.