The Lomax-Claim Model: Bivariate Extension and Applications to Financial Data
The uses of statistical distributions for modeling real phenomena of nature have received considerable attention in the literature. The recent studies have pointed out the potential of statistical distributions in modeling data in applied sciences, particularly in financial sciences. Among them, the...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/9993611 |
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| author | Jin Zhao Humaira Faqiri Zubair Ahmad Walid Emam M. Yusuf A. M. Sharawy |
| author_facet | Jin Zhao Humaira Faqiri Zubair Ahmad Walid Emam M. Yusuf A. M. Sharawy |
| author_sort | Jin Zhao |
| collection | DOAJ |
| description | The uses of statistical distributions for modeling real phenomena of nature have received considerable attention in the literature. The recent studies have pointed out the potential of statistical distributions in modeling data in applied sciences, particularly in financial sciences. Among them, the two-parameter Lomax distribution is one of the prominent models that can be used quite effectively for modeling data in management sciences, banking, finance, and actuarial sciences, among others. In the present article, we introduce a new three-parameter extension of the Lomax distribution via using a class of claim distributions. The new model may be called the Lomax-Claim distribution. The parameters of the Lomax-Claim model are estimated using the maximum likelihood estimation method. The behaviors of the maximum likelihood estimators are examined by conducting a brief Monte Carlo study. The potentiality and applicability of the Lomax claim model are illustrated by analyzing a dataset taken from financial sciences representing the vehicle insurance loss data. For this dataset, the proposed model is compared with the Lomax, power Lomax, transmuted Lomax, and exponentiated Lomax distributions. To show the best fit of the competing distributions, we consider certain analytical tools such as the Anderson–Darling test statistic, Cramer–Von Mises test statistic, and Kolmogorov–Smirnov test statistic. Based on these analytical measures, we observed that the new model outperforms the competitive models. Furthermore, a bivariate extension of the proposed model called the Farlie–Gumble–Morgenstern bivariate Lomax-Claim distribution is also introduced, and different shapes for the density function are plotted. An application of the bivariate model to GDP and export of goods and services is provided. |
| format | Article |
| id | doaj-art-c9c00fb1bd674499a82bd206434e2743 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-c9c00fb1bd674499a82bd206434e27432025-02-03T00:58:59ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/99936119993611The Lomax-Claim Model: Bivariate Extension and Applications to Financial DataJin Zhao0Humaira Faqiri1Zubair Ahmad2Walid Emam3M. Yusuf4A. M. Sharawy5School of Finance, Shanghai Lixin University of Accounting and Finance, Shanghai, ChinaEducation Faculty, Farah Institute of Higher Education, Farah, AfghanistanDepartment of Statistics, Yazd University, P.O. Box 89175-741, Yazd, IranDepartment of Statistics and Operations Research College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Helwan University, Helwan, EgyptDepartment of Mathematical and Natural Sciences, Faculty of Engineering, Egyptian Russian University, Badr, EgyptThe uses of statistical distributions for modeling real phenomena of nature have received considerable attention in the literature. The recent studies have pointed out the potential of statistical distributions in modeling data in applied sciences, particularly in financial sciences. Among them, the two-parameter Lomax distribution is one of the prominent models that can be used quite effectively for modeling data in management sciences, banking, finance, and actuarial sciences, among others. In the present article, we introduce a new three-parameter extension of the Lomax distribution via using a class of claim distributions. The new model may be called the Lomax-Claim distribution. The parameters of the Lomax-Claim model are estimated using the maximum likelihood estimation method. The behaviors of the maximum likelihood estimators are examined by conducting a brief Monte Carlo study. The potentiality and applicability of the Lomax claim model are illustrated by analyzing a dataset taken from financial sciences representing the vehicle insurance loss data. For this dataset, the proposed model is compared with the Lomax, power Lomax, transmuted Lomax, and exponentiated Lomax distributions. To show the best fit of the competing distributions, we consider certain analytical tools such as the Anderson–Darling test statistic, Cramer–Von Mises test statistic, and Kolmogorov–Smirnov test statistic. Based on these analytical measures, we observed that the new model outperforms the competitive models. Furthermore, a bivariate extension of the proposed model called the Farlie–Gumble–Morgenstern bivariate Lomax-Claim distribution is also introduced, and different shapes for the density function are plotted. An application of the bivariate model to GDP and export of goods and services is provided.http://dx.doi.org/10.1155/2021/9993611 |
| spellingShingle | Jin Zhao Humaira Faqiri Zubair Ahmad Walid Emam M. Yusuf A. M. Sharawy The Lomax-Claim Model: Bivariate Extension and Applications to Financial Data Complexity |
| title | The Lomax-Claim Model: Bivariate Extension and Applications to Financial Data |
| title_full | The Lomax-Claim Model: Bivariate Extension and Applications to Financial Data |
| title_fullStr | The Lomax-Claim Model: Bivariate Extension and Applications to Financial Data |
| title_full_unstemmed | The Lomax-Claim Model: Bivariate Extension and Applications to Financial Data |
| title_short | The Lomax-Claim Model: Bivariate Extension and Applications to Financial Data |
| title_sort | lomax claim model bivariate extension and applications to financial data |
| url | http://dx.doi.org/10.1155/2021/9993611 |
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