Analysis of Adaptive Progressive Type-II Hybrid Censored Dagum Data with Applications
In life testing and reliability studies, obtaining whole data always takes a long time and lots of monetary and human resources. In this case, the experimenters prefer to gather data using censoring schemes that make a balance between the length of the test, the desired sample size, and the cost. La...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/10/2146 |
| _version_ | 1797469830768492544 |
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| author | Heba S. Mohammed Mazen Nassar Refah Alotaibi Ahmed Elshahhat |
| author_facet | Heba S. Mohammed Mazen Nassar Refah Alotaibi Ahmed Elshahhat |
| author_sort | Heba S. Mohammed |
| collection | DOAJ |
| description | In life testing and reliability studies, obtaining whole data always takes a long time and lots of monetary and human resources. In this case, the experimenters prefer to gather data using censoring schemes that make a balance between the length of the test, the desired sample size, and the cost. Lately, an adaptive progressive type-II hybrid censoring scheme is suggested to enhance the efficiency of the statistical inference. By utilizing this scheme, this paper seeks to investigate classical and Bayesian estimations of the Dagum distribution. The maximum likelihood and Bayesian estimation methods are considered to estimate the distribution parameters and some reliability indices. The Bayesian estimation is developed under the assumption of independent gamma priors and by employing symmetric and asymmetric loss functions. Due to the tough form of the joint posterior distribution, the Markov chain Monte Carlo technique is implemented to gather samples from the full conditional distributions and in turn obtain the Bayes estimates. The approximate confidence intervals and the highest posterior density credible intervals are also obtained. The effectiveness of the various suggested methods is compared through a simulated study. The optimal progressive censoring plans are also shown, and number of optimality criteria are explored. To demonstrate the applicability of the suggested point and interval estimators, two real data sets are also examined. The outcomes of the simulation study and data analysis demonstrated that the proposed scheme is adaptable and very helpful in ending the experiment when the experimenter’s primary concern is the number of failures. |
| first_indexed | 2024-03-09T19:25:38Z |
| format | Article |
| id | doaj.art-338bf39d4fe445aa981750e7fda369b2 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T19:25:38Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-338bf39d4fe445aa981750e7fda369b22023-11-24T02:53:12ZengMDPI AGSymmetry2073-89942022-10-011410214610.3390/sym14102146Analysis of Adaptive Progressive Type-II Hybrid Censored Dagum Data with ApplicationsHeba S. Mohammed0Mazen Nassar1Refah Alotaibi2Ahmed Elshahhat3Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaFaculty of Technology and Development, Zagazig University, Zagazig 44519, EgyptIn life testing and reliability studies, obtaining whole data always takes a long time and lots of monetary and human resources. In this case, the experimenters prefer to gather data using censoring schemes that make a balance between the length of the test, the desired sample size, and the cost. Lately, an adaptive progressive type-II hybrid censoring scheme is suggested to enhance the efficiency of the statistical inference. By utilizing this scheme, this paper seeks to investigate classical and Bayesian estimations of the Dagum distribution. The maximum likelihood and Bayesian estimation methods are considered to estimate the distribution parameters and some reliability indices. The Bayesian estimation is developed under the assumption of independent gamma priors and by employing symmetric and asymmetric loss functions. Due to the tough form of the joint posterior distribution, the Markov chain Monte Carlo technique is implemented to gather samples from the full conditional distributions and in turn obtain the Bayes estimates. The approximate confidence intervals and the highest posterior density credible intervals are also obtained. The effectiveness of the various suggested methods is compared through a simulated study. The optimal progressive censoring plans are also shown, and number of optimality criteria are explored. To demonstrate the applicability of the suggested point and interval estimators, two real data sets are also examined. The outcomes of the simulation study and data analysis demonstrated that the proposed scheme is adaptable and very helpful in ending the experiment when the experimenter’s primary concern is the number of failures.https://www.mdpi.com/2073-8994/14/10/2146Dagum distributionadaptive progressive type-II hybrid censoringlikelihood estimationBayesian estimationoptimum progressive censoring |
| spellingShingle | Heba S. Mohammed Mazen Nassar Refah Alotaibi Ahmed Elshahhat Analysis of Adaptive Progressive Type-II Hybrid Censored Dagum Data with Applications Symmetry Dagum distribution adaptive progressive type-II hybrid censoring likelihood estimation Bayesian estimation optimum progressive censoring |
| title | Analysis of Adaptive Progressive Type-II Hybrid Censored Dagum Data with Applications |
| title_full | Analysis of Adaptive Progressive Type-II Hybrid Censored Dagum Data with Applications |
| title_fullStr | Analysis of Adaptive Progressive Type-II Hybrid Censored Dagum Data with Applications |
| title_full_unstemmed | Analysis of Adaptive Progressive Type-II Hybrid Censored Dagum Data with Applications |
| title_short | Analysis of Adaptive Progressive Type-II Hybrid Censored Dagum Data with Applications |
| title_sort | analysis of adaptive progressive type ii hybrid censored dagum data with applications |
| topic | Dagum distribution adaptive progressive type-II hybrid censoring likelihood estimation Bayesian estimation optimum progressive censoring |
| url | https://www.mdpi.com/2073-8994/14/10/2146 |
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