A New Class of Bivariate Distributions: Properties, Estimation, and Modeling
The development of bivariate distributions is a challenging area of research, and a novel class of bivariate distributions is proposed in this paper. Certain useful mathematical characteristics of the proposed class of bivariate distributions are explored in general. These properties include the joi...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/24/4021 |
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| author | Jumanah Ahmed Darwish Saman Hanif Shahbaz Muhammad Qaiser Shahbaz |
| author_facet | Jumanah Ahmed Darwish Saman Hanif Shahbaz Muhammad Qaiser Shahbaz |
| author_sort | Jumanah Ahmed Darwish |
| collection | DOAJ |
| description | The development of bivariate distributions is a challenging area of research, and a novel class of bivariate distributions is proposed in this paper. Certain useful mathematical characteristics of the proposed class of bivariate distributions are explored in general. These properties include the joint and conditional and joint survival function moments and measures of dependence. The parameters of the proposed class of distributions are estimated using the maximum likelihood method of estimation. A multivariate version of the proposed class is also proposed, and some necessary properties are discussed. The multivariate dependence measures are obtained for the proposed multivariate class of distributions. A new bivariate power function distribution is proposed using the power function distribution as a baseline distribution in the proposed bivariate class. Some useful properties of the proposed bivariate distribution are studied. The parameters of the proposed bivariate distribution are estimated using the maximum likelihood method. An extensive simulation study has been conducted to see the performance of the estimation method. The new bivariate power function distribution is used to model some real data. |
| format | Article |
| id | doaj-art-5207e40a09ff4531affd3317d556e2fc |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-5207e40a09ff4531affd3317d556e2fc2025-08-20T02:56:50ZengMDPI AGMathematics2227-73902024-12-011224402110.3390/math12244021A New Class of Bivariate Distributions: Properties, Estimation, and ModelingJumanah Ahmed Darwish0Saman Hanif Shahbaz1Muhammad Qaiser Shahbaz2Department of Mathematics and Statistics, University of Jeddah, Jeddah 21959, Saudi ArabiaDepartment of Statistics, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Statistics, King Abdulaziz University, Jeddah 21589, Saudi ArabiaThe development of bivariate distributions is a challenging area of research, and a novel class of bivariate distributions is proposed in this paper. Certain useful mathematical characteristics of the proposed class of bivariate distributions are explored in general. These properties include the joint and conditional and joint survival function moments and measures of dependence. The parameters of the proposed class of distributions are estimated using the maximum likelihood method of estimation. A multivariate version of the proposed class is also proposed, and some necessary properties are discussed. The multivariate dependence measures are obtained for the proposed multivariate class of distributions. A new bivariate power function distribution is proposed using the power function distribution as a baseline distribution in the proposed bivariate class. Some useful properties of the proposed bivariate distribution are studied. The parameters of the proposed bivariate distribution are estimated using the maximum likelihood method. An extensive simulation study has been conducted to see the performance of the estimation method. The new bivariate power function distribution is used to model some real data.https://www.mdpi.com/2227-7390/12/24/4021class of distributionsbivariate distributionsdependence measuresreliability analysismaximum likelihood estimationpower function distribution |
| spellingShingle | Jumanah Ahmed Darwish Saman Hanif Shahbaz Muhammad Qaiser Shahbaz A New Class of Bivariate Distributions: Properties, Estimation, and Modeling Mathematics class of distributions bivariate distributions dependence measures reliability analysis maximum likelihood estimation power function distribution |
| title | A New Class of Bivariate Distributions: Properties, Estimation, and Modeling |
| title_full | A New Class of Bivariate Distributions: Properties, Estimation, and Modeling |
| title_fullStr | A New Class of Bivariate Distributions: Properties, Estimation, and Modeling |
| title_full_unstemmed | A New Class of Bivariate Distributions: Properties, Estimation, and Modeling |
| title_short | A New Class of Bivariate Distributions: Properties, Estimation, and Modeling |
| title_sort | new class of bivariate distributions properties estimation and modeling |
| topic | class of distributions bivariate distributions dependence measures reliability analysis maximum likelihood estimation power function distribution |
| url | https://www.mdpi.com/2227-7390/12/24/4021 |
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