%0 Journal Article
%T On the Mean Residual Life Function and Stress and Strength Analysis under Different Loss Function for Lindley Distribution
%A Sajid Ali
%J Journal of Quality and Reliability Engineering
%D 2013
%R 10.1155/2013/190437
%X Purpose. Mathematical properties of Lindley distribution are derived under different loss functions. These properties include mean residual life function, Lorenz curve, stress and strength characteristic, and their respective posterior risk via simulation scheme. Methodology. Bayesian approach is used for the reliability characteristics. Results are compared on the basis of posterior risk. Findings. Using prior information on the parameter of Lindley distribution, Bayes estimates for reliability characteristics are compared under different loss functions. Practical Implications. Since Lindley distribution is a mixture of gamma and exponential distribution, so Bayesian estimation of reliability characteristics will have a great implication in reliability theory. Originality. A real life application to waiting time data at the bank is also described for the developed procedures. This study is useful for researcher and practitioner in reliability theory. 1. Introduction Exponential distribution is frequently used as a lifetime distribution in statistics and applied areas; the Lindley distribution has been ignored in the literature since 1958. Lindley distribution originally developed by Lindley [1] and some classical statistic properties are investigated by Ghitany et al. [2]. Sankaran [3] introduced a discrete version of Lindley distribution known as discrete Poisson-Lindley distribution, and Ghitany and Al-Mutairi [4] described some estimation methods. The distribution of zero-truncated Poisson-Lindley was introduced by Ghitany et al. [5] who used the distribution for modeling count data in the case where the distribution has to be adjusted for the count of missing zeros. Zamani and Ismail [6] introduced negative binomial distribution as an alternative to zero-truncated Poisson-Lindley distribution. Recently, Ghitany et al. [7] introduced a two-parameter weighted Lindley distribution and pointed that Lindley distribution is particularly useful in modelling biological data from mortality studies. The rest of the study is organized as follows. Section 2 deals with the derivation of posterior distribution using different noninformative and informative priors. Using different loss functions, the Bayes estimators and their respective posterior risks are discussed in Section 3. Elicitation of hyperparameter is also discussed in Section 3. Simulation study of Bayes estimates of mean residual life and their posterior risks is performed in Section 4. Lorenz curve discussion for Lindley distribution is given in Section 5 while stress and strength reliability
%U http://www.hindawi.com/journals/jqre/2013/190437/