The Unit Quasi-Lindley Distribution: Properties, Inference, and Applications to Real Data

Abstract

This article presents the Unit Quasi-Lindley distribution, a two-parameter model for continuous data defined on the unit interval, derived via an exponential transformation of the Quasi-Lindley distribution. Fundamental properties are established, including moments, the generating function, and the quantile function, along with an analysis of the shapes of the density and hazard rate functions, which encompass monotonic and bathtub-shaped patterns. The model parameters are estimated using maximum likelihood, and the efficiency of the estimators is evaluated through Monte Carlo simulation studies. Two applications to real-world datasets demonstrate that the proposed distribution provides a superior fit compared to existing unit-interval distributions in the literature.