Statistical Properties and Applications of a New Truncated Zubair- Generalized Family of Distributions
This paper proposed a truncated family of probability distributions named the doubly truncated Zubair-generalized family of truncated distributions. Certain properties of doubly truncated Zubair-Generalized family of truncated distributions are worked on. These properties are the quantile, median, t...
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| Format: | Article |
| Language: | English |
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The Scientific Association for Studies and Applied Research
2025-04-01
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| Series: | Computational Journal of Mathematical and Statistical Sciences |
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| Online Access: | https://cjmss.journals.ekb.eg/article_401330.html |
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| author | Doaa Soliman Mai A. Hegazy Gannat R. AL-Dayian Abeer A. EL-Helbawy |
| author_facet | Doaa Soliman Mai A. Hegazy Gannat R. AL-Dayian Abeer A. EL-Helbawy |
| author_sort | Doaa Soliman |
| collection | DOAJ |
| description | This paper proposed a truncated family of probability distributions named the doubly truncated Zubair-generalized family of truncated distributions. Certain properties of doubly truncated Zubair-Generalized family of truncated distributions are worked on. These properties are the quantile, median, the non-central moments, central moments, order statistics, entropy measures such as R$\acute{e}$nyi, Shannon, Tsallis entropies, also the mean residual life, mean past lifetime and mean time to failure. The doubly truncated Zubair-Weibull distribution is a special sub-model of the doubly truncated Zubair-generalized family. Some important statistical properties of the doubly truncated Zubair-Weibull distribution are studied, such as the reliability, hazard, reversed hazard and cumulative hazard rate functions. In addition, the moments, quantile, order statistics, entropies and some important special sub-models of the doubly truncated Zubair-Weibull distribution are given. The maximum likelihood estimation approach is applied to estimate the unknown parameters, reliability and hazard rate functions. A simulation study is conducted to evaluate the performance of the maximum likelihood estimates. Two life-time real data sets are applied to show the flexibility and applicability of the proposed model. |
| format | Article |
| id | doaj-art-d096c10c92cd4f2eb7da55aaaace99f4 |
| institution | Kabale University |
| issn | 2974-3435 2974-3443 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | The Scientific Association for Studies and Applied Research |
| record_format | Article |
| series | Computational Journal of Mathematical and Statistical Sciences |
| spelling | doaj-art-d096c10c92cd4f2eb7da55aaaace99f42025-08-20T03:40:35ZengThe Scientific Association for Studies and Applied ResearchComputational Journal of Mathematical and Statistical Sciences2974-34352974-34432025-04-014122225710.21608/CJMSS.2024.322714.1073Statistical Properties and Applications of a New Truncated Zubair- Generalized Family of DistributionsDoaa Soliman 0Mai A. Hegazy1 Gannat R. AL-Dayian2Abeer A. EL-Helbawy 3Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Tafahna Al-Ashraf, Egypt Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Tafahna Al-Ashraf, EgyptDepartment of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Cairo, EgyptDepartment of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Cairo, EgyptThis paper proposed a truncated family of probability distributions named the doubly truncated Zubair-generalized family of truncated distributions. Certain properties of doubly truncated Zubair-Generalized family of truncated distributions are worked on. These properties are the quantile, median, the non-central moments, central moments, order statistics, entropy measures such as R$\acute{e}$nyi, Shannon, Tsallis entropies, also the mean residual life, mean past lifetime and mean time to failure. The doubly truncated Zubair-Weibull distribution is a special sub-model of the doubly truncated Zubair-generalized family. Some important statistical properties of the doubly truncated Zubair-Weibull distribution are studied, such as the reliability, hazard, reversed hazard and cumulative hazard rate functions. In addition, the moments, quantile, order statistics, entropies and some important special sub-models of the doubly truncated Zubair-Weibull distribution are given. The maximum likelihood estimation approach is applied to estimate the unknown parameters, reliability and hazard rate functions. A simulation study is conducted to evaluate the performance of the maximum likelihood estimates. Two life-time real data sets are applied to show the flexibility and applicability of the proposed model.https://cjmss.journals.ekb.eg/article_401330.htmltruncated distributionsorder statisticsmaximum likelihood methodmarkov chain monte carlo methodweibull distribution |
| spellingShingle | Doaa Soliman Mai A. Hegazy Gannat R. AL-Dayian Abeer A. EL-Helbawy Statistical Properties and Applications of a New Truncated Zubair- Generalized Family of Distributions Computational Journal of Mathematical and Statistical Sciences truncated distributions order statistics maximum likelihood method markov chain monte carlo method weibull distribution |
| title | Statistical Properties and Applications of a New Truncated Zubair- Generalized Family of Distributions |
| title_full | Statistical Properties and Applications of a New Truncated Zubair- Generalized Family of Distributions |
| title_fullStr | Statistical Properties and Applications of a New Truncated Zubair- Generalized Family of Distributions |
| title_full_unstemmed | Statistical Properties and Applications of a New Truncated Zubair- Generalized Family of Distributions |
| title_short | Statistical Properties and Applications of a New Truncated Zubair- Generalized Family of Distributions |
| title_sort | statistical properties and applications of a new truncated zubair generalized family of distributions |
| topic | truncated distributions order statistics maximum likelihood method markov chain monte carlo method weibull distribution |
| url | https://cjmss.journals.ekb.eg/article_401330.html |
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