Utilizing Empirical Bayes Estimation to Assess Reliability in Inverted Exponentiated Rayleigh Distribution with Progressive Hybrid Censored Medical Data
This study addresses the issue of estimating the shape parameter of the inverted exponentiated Rayleigh distribution, along with the assessment of reliability and failure rate, by utilizing Type-I progressive hybrid censored data. The study explores the estimators based on maximum likelihood, Bayes,...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/9/872 |
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| author | Atef F. Hashem Salem A. Alyami Manal M. Yousef |
| author_facet | Atef F. Hashem Salem A. Alyami Manal M. Yousef |
| author_sort | Atef F. Hashem |
| collection | DOAJ |
| description | This study addresses the issue of estimating the shape parameter of the inverted exponentiated Rayleigh distribution, along with the assessment of reliability and failure rate, by utilizing Type-I progressive hybrid censored data. The study explores the estimators based on maximum likelihood, Bayes, and empirical Bayes methodologies. Additionally, the study focuses on the development of Bayes and empirical Bayes estimators with balanced loss functions. A concrete example based on actual data from the field of medicine is used to illustrate the theoretical insights provided in this study. Monte Carlo simulations are employed to conduct numerical comparisons and evaluate the performance and accuracy of the estimation methods. |
| first_indexed | 2024-03-10T23:02:19Z |
| format | Article |
| id | doaj.art-4e38d15004c146f98fe4d8e404ddf2b8 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T23:02:19Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-4e38d15004c146f98fe4d8e404ddf2b82023-11-19T09:32:53ZengMDPI AGAxioms2075-16802023-09-0112987210.3390/axioms12090872Utilizing Empirical Bayes Estimation to Assess Reliability in Inverted Exponentiated Rayleigh Distribution with Progressive Hybrid Censored Medical DataAtef F. Hashem0Salem A. Alyami1Manal M. Yousef2Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi ArabiaDepartment of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi ArabiaDepartment of Mathematics, Faculty of Science, New Valley University, El-Khargah 72511, EgyptThis study addresses the issue of estimating the shape parameter of the inverted exponentiated Rayleigh distribution, along with the assessment of reliability and failure rate, by utilizing Type-I progressive hybrid censored data. The study explores the estimators based on maximum likelihood, Bayes, and empirical Bayes methodologies. Additionally, the study focuses on the development of Bayes and empirical Bayes estimators with balanced loss functions. A concrete example based on actual data from the field of medicine is used to illustrate the theoretical insights provided in this study. Monte Carlo simulations are employed to conduct numerical comparisons and evaluate the performance and accuracy of the estimation methods.https://www.mdpi.com/2075-1680/12/9/872inverted exponentiated Rayleigh distributionType-I progressive hybrid censoringmaximum likelihood methodempirical Bayes inference |
| spellingShingle | Atef F. Hashem Salem A. Alyami Manal M. Yousef Utilizing Empirical Bayes Estimation to Assess Reliability in Inverted Exponentiated Rayleigh Distribution with Progressive Hybrid Censored Medical Data Axioms inverted exponentiated Rayleigh distribution Type-I progressive hybrid censoring maximum likelihood method empirical Bayes inference |
| title | Utilizing Empirical Bayes Estimation to Assess Reliability in Inverted Exponentiated Rayleigh Distribution with Progressive Hybrid Censored Medical Data |
| title_full | Utilizing Empirical Bayes Estimation to Assess Reliability in Inverted Exponentiated Rayleigh Distribution with Progressive Hybrid Censored Medical Data |
| title_fullStr | Utilizing Empirical Bayes Estimation to Assess Reliability in Inverted Exponentiated Rayleigh Distribution with Progressive Hybrid Censored Medical Data |
| title_full_unstemmed | Utilizing Empirical Bayes Estimation to Assess Reliability in Inverted Exponentiated Rayleigh Distribution with Progressive Hybrid Censored Medical Data |
| title_short | Utilizing Empirical Bayes Estimation to Assess Reliability in Inverted Exponentiated Rayleigh Distribution with Progressive Hybrid Censored Medical Data |
| title_sort | utilizing empirical bayes estimation to assess reliability in inverted exponentiated rayleigh distribution with progressive hybrid censored medical data |
| topic | inverted exponentiated Rayleigh distribution Type-I progressive hybrid censoring maximum likelihood method empirical Bayes inference |
| url | https://www.mdpi.com/2075-1680/12/9/872 |
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