Comparison of Different Confidence Intervals under Type-I Censoring Scheme
In a life testing experiment, the successive failure times at putting n units under test are recorded under consideration that the advance fixed experiment is terminated at time T. This type of censoring scheme, called conventional Type-I censoring scheme, is used widely. In this paper, we assume th...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/1272045 |
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| author | Ali Algarni Abdullah M. Almarashi Debasis Kundu G. A. Abd-Elmougod Sayed Abdel-Khalek |
| author_facet | Ali Algarni Abdullah M. Almarashi Debasis Kundu G. A. Abd-Elmougod Sayed Abdel-Khalek |
| author_sort | Ali Algarni |
| collection | DOAJ |
| description | In a life testing experiment, the successive failure times at putting n units under test are recorded under consideration that the advance fixed experiment is terminated at time T. This type of censoring scheme, called conventional Type-I censoring scheme, is used widely. In this paper, we assume that the items’ failure times are independent and distributed with exponential lifetime distribution with parameter θ. The estimator with maximum likelihood method is obtained in an exact form and its distribution is also obtained with the unknown parameter. We proposed the exact confidence interval, for estimators θ^ and lnθ^, asymptotic confidence intervals, confidence interval under likelihood ratio test, and finally, two bootstrap confidence intervals. Under the Bayesian approach, the unknown parameter is estimated and the corresponding credible interval is obtained considering the prior information formulated with the inverted gamma distribution. The Monte Carlo simulation study is used to compare different methods. Finally, for illustrative purposes, the real dataset is used and analyzed. |
| format | Article |
| id | doaj-art-3a4cdeedfa854c82a956d073c2e27254 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-3a4cdeedfa854c82a956d073c2e272542025-02-03T01:22:58ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/1272045Comparison of Different Confidence Intervals under Type-I Censoring SchemeAli Algarni0Abdullah M. Almarashi1Debasis Kundu2G. A. Abd-Elmougod3Sayed Abdel-Khalek4Department of StatisticsDepartment of StatisticsDepartment of Mathematics and StatisticsMathematics DepartmentMathematics and Statistics DepartmentIn a life testing experiment, the successive failure times at putting n units under test are recorded under consideration that the advance fixed experiment is terminated at time T. This type of censoring scheme, called conventional Type-I censoring scheme, is used widely. In this paper, we assume that the items’ failure times are independent and distributed with exponential lifetime distribution with parameter θ. The estimator with maximum likelihood method is obtained in an exact form and its distribution is also obtained with the unknown parameter. We proposed the exact confidence interval, for estimators θ^ and lnθ^, asymptotic confidence intervals, confidence interval under likelihood ratio test, and finally, two bootstrap confidence intervals. Under the Bayesian approach, the unknown parameter is estimated and the corresponding credible interval is obtained considering the prior information formulated with the inverted gamma distribution. The Monte Carlo simulation study is used to compare different methods. Finally, for illustrative purposes, the real dataset is used and analyzed.http://dx.doi.org/10.1155/2022/1272045 |
| spellingShingle | Ali Algarni Abdullah M. Almarashi Debasis Kundu G. A. Abd-Elmougod Sayed Abdel-Khalek Comparison of Different Confidence Intervals under Type-I Censoring Scheme Journal of Mathematics |
| title | Comparison of Different Confidence Intervals under Type-I Censoring Scheme |
| title_full | Comparison of Different Confidence Intervals under Type-I Censoring Scheme |
| title_fullStr | Comparison of Different Confidence Intervals under Type-I Censoring Scheme |
| title_full_unstemmed | Comparison of Different Confidence Intervals under Type-I Censoring Scheme |
| title_short | Comparison of Different Confidence Intervals under Type-I Censoring Scheme |
| title_sort | comparison of different confidence intervals under type i censoring scheme |
| url | http://dx.doi.org/10.1155/2022/1272045 |
| work_keys_str_mv | AT alialgarni comparisonofdifferentconfidenceintervalsundertypeicensoringscheme AT abdullahmalmarashi comparisonofdifferentconfidenceintervalsundertypeicensoringscheme AT debasiskundu comparisonofdifferentconfidenceintervalsundertypeicensoringscheme AT gaabdelmougod comparisonofdifferentconfidenceintervalsundertypeicensoringscheme AT sayedabdelkhalek comparisonofdifferentconfidenceintervalsundertypeicensoringscheme |