Shrinkage Estimation of the Mean Parameter of the Exponential Distribution under Type-II Hybrid Censored Samples

Accepted June 2026

Abstract

In this paper, we study the problem of estimating the mean parameter of the exponential distribution based on Type-II hybrid censored samples. It is well known that the maximum likelihood estimator (MLE) may exhibit significant bias and large mean squared error (MSE), particularly in small samples or under high levels of censoring. To address these limitations, we develop a class of shrinkage estimators that reduce the influence of censored observations by adopting suitable shrinkage factors. The statistical properties of the proposed estimators are established using the moment generating function, including explicit expressions for bias and MSE. Comparison performance between the proposed estimators and classical estimator is conducted through real-life data examples and simulation studies. The results demonstrate that the shrinkage estimators are better than the MLE in terms of MSE, while also obtaining a noticeable bias reduction.