Abstract
In this paper, the moment-based, maximum likelihood and Bayes estimators for the unknown parameter of the Lindley model based on Type II censored data are discussed. The expectation maximization (EM) algorithm and direct maximization methods are used to obtained the maximum likelihood estimator (MLE). Existence and uniqueness of the moment-based and maximum likelihood estimators are discussed and a bias corrected estimator based on parametric bootstrap is developed. For Bayesian estimation, since the Bayes estimator cannot be obtained in an explicit form, two approximations based on Lindley and the importance sampling methods are used. Asymptotic confidence intervals, bootstrap confidence intervals and credible intervals are also proposed. Based on Type II censored data, the prediction of future observations is discussed. The analysis of a real data has been presented for illustrative purposes. Finally, Monte Carlo simulations are performed to compare the performances of the proposed estimation methods.
Highlights
The Lindley distribution has the probability density function f (x; θ ) = θ2 1+θ (1 + x)e−θ x, x > 0, θ > 0. (1.1)and the cumulative distribution function F
We aim to study the point and interval estimation of the parameter in the Lindley distribution and to study the prediction of future failures based on Type II censored data
We propose a moment-based estimation method and develop the expectation maximization (EM) algorithm for the computation of the maximum likelihood estimator (MLE)
Summary
We aim to study the point and interval estimation of the parameter in the Lindley distribution and to study the prediction of future failures based on Type II censored data. The prediction of future observations is developed based on Type II censored data. The estimation of parameter of the Lindley distribution has been discussed extensively in the literature, a comprehensive comparison of different methods for estimation has not been done. Another contribution of our work is the development of the MBE and proofing the existence and uniqueness of the MBE and MLE.
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