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

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  • Zheng Li

    (Department of Statistics and Actuarial Science, College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
    These authors contributed equally to this work.)

  • Ying-Ying Zhang

    (Yunnan Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University, Kunming 650500, China
    These authors contributed equally to this work.)

  • Ya-Guang Shi

    (Department of Statistics and Actuarial Science, College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China)

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.

Suggested Citation

  • Zheng Li & Ying-Ying Zhang & Ya-Guang Shi, 2025. "Empirical Bayes Estimators for Mean Parameter of Exponential Distribution with Conjugate Inverse Gamma Prior Under Stein’s Loss," Mathematics, MDPI, vol. 13(10), pages 1-23, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1658-:d:1658943
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    References listed on IDEAS

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    1. Marsaglia, George & Tsang, Wai Wan & Wang, Jingbo, 2003. "Evaluating Kolmogorov's Distribution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 8(i18).
    2. Ying-Ying Zhang, 2017. "The Bayes rule of the variance parameter of the hierarchical normal and inverse gamma model under Stein's loss," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(14), pages 7125-7133, July.
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