A New Three-Parameter Generalized Lindley Probability Model With Engineering Applications

Abstract

During recent decades several lifetime distributions of one parameter, two-parameter and three-parameter have been proposed to model engineering data but due to either theoretical nature or the stochastic nature of the distribution, these available distributions are not suitable to model the data. In this paper, an attempt has been made to propose a new three-parameter generalized Lindley distribution which includes several one parameter and two-parameter continuous distributions including exponential, Lindley, Weibull, Power-Lindley and new two-parameter Lindley as particular cases. Descriptive statistical properties including hazard function, mean residual life function, moments and order statistics have been derived and discussed. Fisher’s information matrix and confidence interval of the proposed distribution have been derived. Numerical simulation study has been carried out to know the consistency of maximum likelihood estimators. Maximum likelihood estimation for estimating parameters has been explained. Two under-dispersed real lifetime datasets from the field of engineering have been presented to test the goodness of fit of the proposed distribution over other one parameter, two-parameter and three-parameter lifetime distributions.