Development and Estimation of Weighted Xgamma Exponential Distribution with Applications to Lifetime Data
In this article, we introduce a weighted version of the Xgamma exponential distribution, extending its utility in modeling lifetime data. We derive several important distributional properties of the proposed model, including moments, residual life functions, generating functions, stochastic ordering...
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| Format: | Article |
| Language: | English |
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University of Bologna
2025-04-01
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| Series: | Statistica |
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| Online Access: | https://rivista-statistica.unibo.it/article/view/16940 |
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| author | Abhimanyu Singh Yadav Shivanshi Shukla Neha Jaiswal Sanjay Kumar Singh Debayan Koley |
| author_facet | Abhimanyu Singh Yadav Shivanshi Shukla Neha Jaiswal Sanjay Kumar Singh Debayan Koley |
| author_sort | Abhimanyu Singh Yadav |
| collection | DOAJ |
| description | In this article, we introduce a weighted version of the Xgamma exponential distribution, extending its utility in modeling lifetime data. We derive several important distributional properties of the proposed model, including moments, residual life functions, generating functions, stochastic ordering, aging intensity, and entropy. These properties provide deeper insights into the behavior and structure of the proposed distribution. To estimate the model parameters, we discuss the maximum likelihood estimation approach, focusing on complete sample data. To demonstrate the practical applicability of the proposed distribution, we analyze two real-world lifetime data sets. The performance of the weighted Xgamma exponential distribution is compared with several well-established one- and two-parameter lifetime distributions, along with their weighted versions. Additionally, comparisons are made with length-biased and area-biased lifetime distributions to further assess the robustness of the proposed model. The results of these comparisons indicate that the proposed weighted distribution offers a superior fit, particularly for data sets exhibiting an increasing failure rate. The model’s ability to outperform competing distributions highlights its potential as an effective alternative for analyzing lifetime data in reliability and survival studies. |
| format | Article |
| id | doaj-art-e1c09b63ce444ffcbff925e0a68ea7e1 |
| institution | OA Journals |
| issn | 0390-590X 1973-2201 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | University of Bologna |
| record_format | Article |
| series | Statistica |
| spelling | doaj-art-e1c09b63ce444ffcbff925e0a68ea7e12025-08-20T02:16:39ZengUniversity of BolognaStatistica0390-590X1973-22012025-04-0183424726910.6092/issn.1973-2201/1694015298Development and Estimation of Weighted Xgamma Exponential Distribution with Applications to Lifetime DataAbhimanyu Singh Yadav0Shivanshi Shukla1Neha Jaiswal2Sanjay Kumar Singh3Debayan Koley4Banaras Hindu University, Varanasi, IndiaCentral University of Rajasthan, Ajmer, IndiaBanaras Hindu University, Varanasi, IndiaBanaras Hindu University, Varanasi, IndiaBanaras Hindu University, Varanasi, IndiaIn this article, we introduce a weighted version of the Xgamma exponential distribution, extending its utility in modeling lifetime data. We derive several important distributional properties of the proposed model, including moments, residual life functions, generating functions, stochastic ordering, aging intensity, and entropy. These properties provide deeper insights into the behavior and structure of the proposed distribution. To estimate the model parameters, we discuss the maximum likelihood estimation approach, focusing on complete sample data. To demonstrate the practical applicability of the proposed distribution, we analyze two real-world lifetime data sets. The performance of the weighted Xgamma exponential distribution is compared with several well-established one- and two-parameter lifetime distributions, along with their weighted versions. Additionally, comparisons are made with length-biased and area-biased lifetime distributions to further assess the robustness of the proposed model. The results of these comparisons indicate that the proposed weighted distribution offers a superior fit, particularly for data sets exhibiting an increasing failure rate. The model’s ability to outperform competing distributions highlights its potential as an effective alternative for analyzing lifetime data in reliability and survival studies.https://rivista-statistica.unibo.it/article/view/16940xgamma exponential distributionweighted xgammacharacterizationspoint and interval estimation |
| spellingShingle | Abhimanyu Singh Yadav Shivanshi Shukla Neha Jaiswal Sanjay Kumar Singh Debayan Koley Development and Estimation of Weighted Xgamma Exponential Distribution with Applications to Lifetime Data Statistica xgamma exponential distribution weighted xgamma characterizations point and interval estimation |
| title | Development and Estimation of Weighted Xgamma Exponential Distribution with Applications to Lifetime Data |
| title_full | Development and Estimation of Weighted Xgamma Exponential Distribution with Applications to Lifetime Data |
| title_fullStr | Development and Estimation of Weighted Xgamma Exponential Distribution with Applications to Lifetime Data |
| title_full_unstemmed | Development and Estimation of Weighted Xgamma Exponential Distribution with Applications to Lifetime Data |
| title_short | Development and Estimation of Weighted Xgamma Exponential Distribution with Applications to Lifetime Data |
| title_sort | development and estimation of weighted xgamma exponential distribution with applications to lifetime data |
| topic | xgamma exponential distribution weighted xgamma characterizations point and interval estimation |
| url | https://rivista-statistica.unibo.it/article/view/16940 |
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