Estimation of Unknown Parameters of Truncated Normal Distribution under Adaptive Progressive Type II Censoring Scheme

Siqi Chen and Wenhao Gui
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Siqi Chen: Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China
Wenhao Gui: Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China

Mathematics, 2020, vol. 9, issue 1, 1-33

Abstract: In reality, estimations for the unknown parameters of truncated distribution with censored data have wide utilization. Truncated normal distribution is more suitable to fit lifetime data compared with normal distribution. This article makes statistical inferences on estimating parameters under truncated normal distribution using adaptive progressive type II censored data. First, the estimates are calculated through exploiting maximum likelihood method. The observed and expected Fisher information matrices are derived to establish the asymptotic confidence intervals. Second, Bayesian estimations under three loss functions are also studied. The point estimates are calculated by Lindley approximation. Importance sampling technique is applied to discuss the Bayes estimates and build the associated highest posterior density credible intervals. Bootstrap confidence intervals are constructed for the purpose of comparison. Monte Carlo simulations and data analysis are employed to present the performances of various methods. Finally, we obtain optimal censoring schemes under different criteria.

Keywords: truncated normal distribution; adaptive progressive Type-II censoring; maximum likelihood estimation; fisher information matrix; Bayes estimation; Lindley approximation; importance sampling; Monte Carlo simulation; optimal censoring scheme (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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