Interval Shrinkage Estimation reliability System of Stress-Strengths Models in two parameter Lindley distribution

 The reliability System plays an important role in the reliability of power play models. Reliability System in Stress-Strengths models is a measure of component reliability. This model was first introduced by Birnbaum in 1956. As we know, the Lindley distribution is widely used in reliability theory and many researchers are used this distribution to calculate Stress-Strengths. In 2013 Al Mutairi and Kundu work out on stress-strength reliability for Lindley distribution. In 2017 Rezaei, et al. estimate the stress-strength parameter R=P(Y<X), when the variables X and Y are from General Lindley distribution. There are different methods to estimate R=P(Y<X) such as maximum likelihood, method of moments, Bayesian, and shrinkage estimation. Recently, many researchers consider the interval shrinkage estimation to estimate parameters of statistical distribution. Here, for the first time, we estimate the R=P(X<Y) by using the interval shrinkage estimation in two parameter Lindley distribution. Ghitany et al. in 2008 showed that the behavior of this distribution in data analysis of life data and reliability is better than the exponential distribution. So, we estimate the parameters of Lindley and R=P(X<Y) by using the interval shrinkage and method of moments estimation. In 2013 Shanker, et al. considers two parameter Lindley distribution for modeling waiting and survival time data. [ Downloaded from mmr.khu.ac.ir on 2022-10-03 ] .

Material and methods:

 In statistical inference, choosing the methods of estimation is very essential in the process of it. The interval shrinkage and method of moments estimation for Lindley distribution is obtained. For interval shrinkage estimation, we consider as an interval for parameter.

Results and discussion:

 To compare the estimators, samples with different sizes and values of parameters are generated from two parameter Lindley distribution by applying R software. Consequently, comparison of the estimators, the estimation of parameters and mean square errors of them are accomplished.

Conclusion:

 Simulation and real data methods are used to compare the method of moments and interval shrinkage estimation for estimating parameters of two parameter Lindley distribution. The results show that the interval shrinkage estimator is better than the method of moment estimator. Material and methods In statistical inference, choosing the methods of estimation is very essential in the process of it. The interval shrinkage and method of moments estimation for Lindley distribution is obtained. For interval shrinkage estimation, we consider as an interval for parameter. Results and discussion To compare the estimators, samples with different sizes and values of parameters are generated from two parameter Lindley distribution by applying R software. Consequently, comparison of the estimators, the estimation of parameters and mean square errors of them are accomplished. Conclusion Simulation and real data methods are used to compare the method of moments and interval shrinkage estimation for estimating parameters of two parameter Lindley distribution. The results show that the interval shrinkage estimator is better than the method of moment estimator.