Statistical Properties and Applications of a New Truncated Zubair- Generalized Family of Distributions
Soliman, D., Hegazy, M., AL-Dayian, G., EL-Helbawy, A. (2025). Statistical Properties and Applications of a New Truncated Zubair- Generalized Family of Distributions. EKB Journal Management System, 4(1), 222-257. doi: 10.21608/cjmss.2024.322714.1073
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". EKB Journal Management System, 4, 1, 2025, 222-257. doi: 10.21608/cjmss.2024.322714.1073
Soliman, D., Hegazy, M., AL-Dayian, G., EL-Helbawy, A. (2025). 'Statistical Properties and Applications of a New Truncated Zubair- Generalized Family of Distributions', EKB Journal Management System, 4(1), pp. 222-257. doi: 10.21608/cjmss.2024.322714.1073
Soliman, D., Hegazy, M., AL-Dayian, G., EL-Helbawy, A. Statistical Properties and Applications of a New Truncated Zubair- Generalized Family of Distributions. EKB Journal Management System, 2025; 4(1): 222-257. doi: 10.21608/cjmss.2024.322714.1073

Statistical Properties and Applications of a New Truncated Zubair- Generalized Family of Distributions

Computational Journal of Mathematical and Statistical Sciences
Volume 4, Issue 1, April 2025, Page 222-257  XML PDF (635.91 K)
Document Type: Original Article
DOI: 10.21608/cjmss.2024.322714.1073
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Authors
Doaa Soliman1; Mai A. Hegazyorcid 2; Gannat R. AL-Dayianorcid 3; Abeer A. EL-Helbawy email orcid 3
1Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Tafahna Al-Ashraf, Egypt
2Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Tafahna Al-Ashraf, Egypt
3Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Cairo, Egypt
Abstract
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.
Keywords
Truncated distributions; Order statistics; Maximum likelihood method; Markov Chain Monte Carlo method; Weibull distribution
Statistics
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