Statistical Inference for Lindley Model based on Type II Censored Data

• Main Authors: A. Asgharzadeh, H.K.T. Ng, R. Valiollahi, M. Azizpour
• Format: Article
• Language: English
• Published: Atlantis Press 2017-05-01
• Series: Journal of Statistical Theory and Applications (JSTA)
• Subjects: Lindley model; Type II censoring; Maximum likelihood estimator; Bayes estimator; Importance Sampling.
• Online Access: https://www.atlantis-press.com/article/25878524.pdf

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.