A Chen-Lindley Distribution: Statistical Inference And Its Applications

The parametric modeling of complex system reliability,such as series systems with dependent,independent components or parallel systems,is still an important aspect of reliability engineering,and recent research has made substantial progress in this field.However,having a flexible compound model with fewer parameters is important.In this thesis,we develop and investigate a novel lifetime distribution based on the mixture technique to overcome the limitations of two traditional models,the Chen and Lindley distributions.The proposed model,namely,the Chen-Lindley distribution,is more flexible and will be good for modeling two independent component series system or failure times with one or two modes of failure.It has decreasing,increasing and bathtub shapes failure rate.We derive some model properties,such as the quantile function,moments,moment generating function,entropy,mean residual life,and mean time to failure.We report some simulation findings for mean residual life and mean time to failure to examine how the properties change with different sample sizes and parameter settings.We estimate the model’s parameters considering censored and non-censored datasets using Bayesian and maximum likelihood methods.We conduct simulation experiments to evaluate the proposed estimation methods for various parameter and sample size settings.We provide real data applications of the proposed distribution to demonstrate its applicability in solving real problems.We compare the performance of our proposed Chen-Lindley distribution to that of the three-parameter additive Weibull-Lindley distribution.On censored psychiatric patient data and non-censored electrical appliance data,the novel distribution outperforms the competing Weibull-Lindley model.