Statistical Inference of Truncated Normal Distribution Based on the Generalized Progressive Hybrid Censoring

• Main Authors: Xinyi Zeng, Wenhao Gui
• Format: Article
• Language: English
• Published: MDPI AG 2021-02-01
• Series: Entropy
• Subjects: truncated normal distribution; generalized progressive hybrid censoring scheme; expectation maximization algorithm; Bayesian estimate; Tierney and Kadane approximation; importance sampling
• Online Access: https://www.mdpi.com/1099-4300/23/2/186

In this paper, the parameter estimation problem of a truncated normal distribution is discussed based on the generalized progressive hybrid censored data. The desired maximum likelihood estimates of unknown quantities are firstly derived through the Newton–Raphson algorithm and the expectation maximization algorithm. Based on the asymptotic normality of the maximum likelihood estimators, we develop the asymptotic confidence intervals. The percentile bootstrap method is also employed in the case of the small sample size. Further, the Bayes estimates are evaluated under various loss functions like squared error, general entropy, and linex loss functions. Tierney and Kadane approximation, as well as the importance sampling approach, is applied to obtain the Bayesian estimates under proper prior distributions. The associated Bayesian credible intervals are constructed in the meantime. Extensive numerical simulations are implemented to compare the performance of different estimation methods. Finally, an authentic example is analyzed to illustrate the inference approaches.