Empirical Bayes Estimators for Mean Parameter of Exponential Distribution with Conjugate Inverse Gamma Prior Under Stein’s Loss

Zheng Li, Ying-Ying Zhang () and Ya-Guang Shi
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Zheng Li: Department of Statistics and Actuarial Science, College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
Ying-Ying Zhang: Yunnan Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University, Kunming 650500, China
Ya-Guang Shi: Department of Statistics and Actuarial Science, College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Mathematics, 2025, vol. 13, issue 10, 1-23

Abstract: A Bayes estimator for a mean parameter of an exponential distribution is calculated using Stein’s loss, which equally penalizes gross overestimation and underestimation. A corresponding Posterior Expected Stein’s Loss (PESL) is also determined. Additionally, a Bayes estimator for a mean parameter is obtained under a squared error loss along with its corresponding PESL. Furthermore, two methods are used to derive empirical Bayes estimators for the mean parameter of the exponential distribution with an inverse gamma prior. Numerical simulations are conducted to illustrate five aspects. Finally, theoretical studies are illustrated using Static Fatigue 90% Stress Level data.

Keywords: empirical Bayes estimators; exponential-inverse gamma model; method of maximum likelihood estimation (MLE); method of moments; Stein’s loss (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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