A study of weighted Lindley distribution: Bayesian approach

Abstract

A weighted version of Lindley Distribution has been presented in this paper, offering a new single-parameter lifetime distribution. The expressions for the moment generating function (mgf), cumulant generating function (cgf), characteristic function, moments, reliability and hazard rate functions of the new weighted Lindley distribution have also been obtained. Tierney and Kadane approximation method has been used to derive Bayes estimators for its parameter (θ), reliability function R(t), and hazard rate function h(t) under three priors namely uniform, exponential and gamma. The findings have been illustrated using various randomly produced data sets from the proposed model using simulation technique, with each sample replicated 10,000 times. The Bayes Risks have been estimated under Squared Error Loss Function (SELF). Two real life data sets have further been used to illustrate its utility. It is finally concluded that gamma prior outperforms uniform and exponential priors for computing the Bayes estimates of the parameter θ, reliability function R(t) and hazard rate function h(t) of the proposed weighted Lindley distribution.