Stress-Strength Reliability of Two-Parameter Exponential Distribution Based on Progres- sively Type-II Censored Data
Introduction: Stress-strength models has achieved considerable attention in recent years due to its applicability in various areas like engineering, quality control, biology, genetics, medicine etc. This paper investigates estimation of the stress-strength reliability parameter in two-parameter ex...
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Tehran University of Medical Sciences
2024-12-01
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| Series: | Journal of Biostatistics and Epidemiology |
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| Online Access: | https://jbe.tums.ac.ir/index.php/jbe/article/view/1431 |
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| author | Sajad Rostamian |
| author_facet | Sajad Rostamian |
| author_sort | Sajad Rostamian |
| collection | DOAJ |
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Introduction: Stress-strength models has achieved considerable attention in recent years due to its applicability in various areas like engineering, quality control, biology, genetics, medicine etc. This paper investigates estimation of the stress-strength reliability parameter in two-parameter exponential distributions under progressively type-II censored samples.
Methods: The maximum likelihood and the best linear unbiased estimates of are obtained, and the Bayes estimates of are computed under the squared error, linear-exponential, and Stein loss functions. Also, confidence intervals of stress-strength reliability such as the bootstrap confidence intervals, highest posterior density credible interval, and confidence interval based on the generalized pivotal quantity are obtained. Results: Using a simulation study, the point estimators and confidence intervals are evaluated and compared. A set of real data is presented for better clarification of the issue.
Conclusion: The results demonstrated that with increasing the sample size, in almost cases the estimated
risk of all the estimators decrease. Also, in almost all cases the Bayes estimator under the linear-exponential
loss function has smaller estimated risk than the other estimators. Based on our simulation, the expected
lengths of all intervals tend to decrease when the sample size increases. Moreover, the highest posterior density confidence intervals are shorter than the others intervals for all the values of P(Y<X).
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| format | Article |
| id | doaj-art-c535abb882ed455bbdf6fb59ab9054c4 |
| institution | Kabale University |
| issn | 2383-4196 2383-420X |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Tehran University of Medical Sciences |
| record_format | Article |
| series | Journal of Biostatistics and Epidemiology |
| spelling | doaj-art-c535abb882ed455bbdf6fb59ab9054c42025-01-06T08:40:29ZengTehran University of Medical SciencesJournal of Biostatistics and Epidemiology2383-41962383-420X2024-12-0110110.18502/jbe.v10i1.17154Stress-Strength Reliability of Two-Parameter Exponential Distribution Based on Progres- sively Type-II Censored DataSajad Rostamian0Department of Statistics, Songhor va Koliyiayi Branch, Islamic Azad University, Songhor, Iran Introduction: Stress-strength models has achieved considerable attention in recent years due to its applicability in various areas like engineering, quality control, biology, genetics, medicine etc. This paper investigates estimation of the stress-strength reliability parameter in two-parameter exponential distributions under progressively type-II censored samples. Methods: The maximum likelihood and the best linear unbiased estimates of are obtained, and the Bayes estimates of are computed under the squared error, linear-exponential, and Stein loss functions. Also, confidence intervals of stress-strength reliability such as the bootstrap confidence intervals, highest posterior density credible interval, and confidence interval based on the generalized pivotal quantity are obtained. Results: Using a simulation study, the point estimators and confidence intervals are evaluated and compared. A set of real data is presented for better clarification of the issue. Conclusion: The results demonstrated that with increasing the sample size, in almost cases the estimated risk of all the estimators decrease. Also, in almost all cases the Bayes estimator under the linear-exponential loss function has smaller estimated risk than the other estimators. Based on our simulation, the expected lengths of all intervals tend to decrease when the sample size increases. Moreover, the highest posterior density confidence intervals are shorter than the others intervals for all the values of P(Y<X). https://jbe.tums.ac.ir/index.php/jbe/article/view/1431Generalized pivotal quantity, Bayesian estimation, Gibbs sampling, Progressively type-ΙΙ censoring, Two-parameter exponential distribution |
| spellingShingle | Sajad Rostamian Stress-Strength Reliability of Two-Parameter Exponential Distribution Based on Progres- sively Type-II Censored Data Journal of Biostatistics and Epidemiology Generalized pivotal quantity, Bayesian estimation, Gibbs sampling, Progressively type-ΙΙ censoring, Two-parameter exponential distribution |
| title | Stress-Strength Reliability of Two-Parameter Exponential Distribution Based on Progres- sively Type-II Censored Data |
| title_full | Stress-Strength Reliability of Two-Parameter Exponential Distribution Based on Progres- sively Type-II Censored Data |
| title_fullStr | Stress-Strength Reliability of Two-Parameter Exponential Distribution Based on Progres- sively Type-II Censored Data |
| title_full_unstemmed | Stress-Strength Reliability of Two-Parameter Exponential Distribution Based on Progres- sively Type-II Censored Data |
| title_short | Stress-Strength Reliability of Two-Parameter Exponential Distribution Based on Progres- sively Type-II Censored Data |
| title_sort | stress strength reliability of two parameter exponential distribution based on progres sively type ii censored data |
| topic | Generalized pivotal quantity, Bayesian estimation, Gibbs sampling, Progressively type-ΙΙ censoring, Two-parameter exponential distribution |
| url | https://jbe.tums.ac.ir/index.php/jbe/article/view/1431 |
| work_keys_str_mv | AT sajadrostamian stressstrengthreliabilityoftwoparameterexponentialdistributionbasedonprogressivelytypeiicensoreddata |