Empirical Bayes Estimators for Mean Parameter of Exponential Distribution with Conjugate Inverse Gamma Prior Under Stein’s Loss
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...
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MDPI AG
2025-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/10/1658 |
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| author | Zheng Li Ying-Ying Zhang Ya-Guang Shi |
| author_facet | Zheng Li Ying-Ying Zhang Ya-Guang Shi |
| author_sort | Zheng Li |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0c68ddb07f624f6a9032cd5d4d9eb8ef |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-0c68ddb07f624f6a9032cd5d4d9eb8ef2025-08-20T01:56:19ZengMDPI AGMathematics2227-73902025-05-011310165810.3390/math13101658Empirical Bayes Estimators for Mean Parameter of Exponential Distribution with Conjugate Inverse Gamma Prior Under Stein’s LossZheng Li0Ying-Ying Zhang1Ya-Guang Shi2Department of Statistics and Actuarial Science, College of Mathematics and Statistics, Chongqing University, Chongqing 401331, ChinaYunnan Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University, Kunming 650500, ChinaDepartment of Statistics and Actuarial Science, College of Mathematics and Statistics, Chongqing University, Chongqing 401331, ChinaA 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.https://www.mdpi.com/2227-7390/13/10/1658empirical Bayes estimatorsexponential-inverse gamma modelmethod of maximum likelihood estimation (MLE)method of momentsStein’s loss |
| spellingShingle | Zheng Li Ying-Ying Zhang Ya-Guang Shi Empirical Bayes Estimators for Mean Parameter of Exponential Distribution with Conjugate Inverse Gamma Prior Under Stein’s Loss Mathematics empirical Bayes estimators exponential-inverse gamma model method of maximum likelihood estimation (MLE) method of moments Stein’s loss |
| title | Empirical Bayes Estimators for Mean Parameter of Exponential Distribution with Conjugate Inverse Gamma Prior Under Stein’s Loss |
| title_full | Empirical Bayes Estimators for Mean Parameter of Exponential Distribution with Conjugate Inverse Gamma Prior Under Stein’s Loss |
| title_fullStr | Empirical Bayes Estimators for Mean Parameter of Exponential Distribution with Conjugate Inverse Gamma Prior Under Stein’s Loss |
| title_full_unstemmed | Empirical Bayes Estimators for Mean Parameter of Exponential Distribution with Conjugate Inverse Gamma Prior Under Stein’s Loss |
| title_short | Empirical Bayes Estimators for Mean Parameter of Exponential Distribution with Conjugate Inverse Gamma Prior Under Stein’s Loss |
| title_sort | empirical bayes estimators for mean parameter of exponential distribution with conjugate inverse gamma prior under stein s loss |
| topic | empirical Bayes estimators exponential-inverse gamma model method of maximum likelihood estimation (MLE) method of moments Stein’s loss |
| url | https://www.mdpi.com/2227-7390/13/10/1658 |
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