A Bounded Lifetime Distribution Specified by a Trigonometric Function: Properties, Regression Model, and Applications
Trigonometric functions have gained considerable attention in recent studies for developing new lifetime distributions. This is due to their parsimonious framework, mathematical tractability, and flexibility of the newly developed distributions. In this paper, the Sine-generated family is used to cr...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2024/5583105 |
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| author | Simon A. Ogumeyo Festus C. Opone Abdul Ghaniyyu Abubakari Jacob C. Ehiwario |
| author_facet | Simon A. Ogumeyo Festus C. Opone Abdul Ghaniyyu Abubakari Jacob C. Ehiwario |
| author_sort | Simon A. Ogumeyo |
| collection | DOAJ |
| description | Trigonometric functions have gained considerable attention in recent studies for developing new lifetime distributions. This is due to their parsimonious framework, mathematical tractability, and flexibility of the newly developed distributions. In this paper, the Sine-generated family is used to create a new bounded lifetime distribution, known as Sine-Marshall–Olkin Topp–Leone distribution, for modeling data defined on the unit interval. Some statistical properties of the new bounded distribution, including quantile function, ordinary moments, incomplete moments, moment-generating functions, inequality measures, Rényi entropy, and probability weighted moments are derived. Seven methods of parameter estimation, including maximum likelihood, ordinary least squares, weighted least squares, moment product spacing, Anderson–Darling, and Cramér–von Mises estimators are used to estimate the parameters of the new distribution. The behavior of the estimators obtained from the estimation methods are investigated using Monte Carlo simulation studies. The results show that the estimation methods are asymptotically efficient and consistent. The flexibility of the new bounded distribution is examined via data fitting using two proportional datasets. The results of the fittings show that the new bounded distribution performs significantly better than the competing bounded lifetime distributions. Finally, Sine-Marshall–Olkin Topp–Leone regression model is presented as an alternative to the beta and Kumaraswamy regression models. |
| format | Article |
| id | doaj-art-98cc361d54e1426395e71b1e858a6b4f |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-98cc361d54e1426395e71b1e858a6b4f2025-02-03T09:38:40ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252024-01-01202410.1155/2024/5583105A Bounded Lifetime Distribution Specified by a Trigonometric Function: Properties, Regression Model, and ApplicationsSimon A. Ogumeyo0Festus C. Opone1Abdul Ghaniyyu Abubakari2Jacob C. Ehiwario3Department of MathematicsDepartment of StatisticsDepartment of Statistics and Actuarial ScienceDepartment of StatisticsTrigonometric functions have gained considerable attention in recent studies for developing new lifetime distributions. This is due to their parsimonious framework, mathematical tractability, and flexibility of the newly developed distributions. In this paper, the Sine-generated family is used to create a new bounded lifetime distribution, known as Sine-Marshall–Olkin Topp–Leone distribution, for modeling data defined on the unit interval. Some statistical properties of the new bounded distribution, including quantile function, ordinary moments, incomplete moments, moment-generating functions, inequality measures, Rényi entropy, and probability weighted moments are derived. Seven methods of parameter estimation, including maximum likelihood, ordinary least squares, weighted least squares, moment product spacing, Anderson–Darling, and Cramér–von Mises estimators are used to estimate the parameters of the new distribution. The behavior of the estimators obtained from the estimation methods are investigated using Monte Carlo simulation studies. The results show that the estimation methods are asymptotically efficient and consistent. The flexibility of the new bounded distribution is examined via data fitting using two proportional datasets. The results of the fittings show that the new bounded distribution performs significantly better than the competing bounded lifetime distributions. Finally, Sine-Marshall–Olkin Topp–Leone regression model is presented as an alternative to the beta and Kumaraswamy regression models.http://dx.doi.org/10.1155/2024/5583105 |
| spellingShingle | Simon A. Ogumeyo Festus C. Opone Abdul Ghaniyyu Abubakari Jacob C. Ehiwario A Bounded Lifetime Distribution Specified by a Trigonometric Function: Properties, Regression Model, and Applications International Journal of Mathematics and Mathematical Sciences |
| title | A Bounded Lifetime Distribution Specified by a Trigonometric Function: Properties, Regression Model, and Applications |
| title_full | A Bounded Lifetime Distribution Specified by a Trigonometric Function: Properties, Regression Model, and Applications |
| title_fullStr | A Bounded Lifetime Distribution Specified by a Trigonometric Function: Properties, Regression Model, and Applications |
| title_full_unstemmed | A Bounded Lifetime Distribution Specified by a Trigonometric Function: Properties, Regression Model, and Applications |
| title_short | A Bounded Lifetime Distribution Specified by a Trigonometric Function: Properties, Regression Model, and Applications |
| title_sort | bounded lifetime distribution specified by a trigonometric function properties regression model and applications |
| url | http://dx.doi.org/10.1155/2024/5583105 |
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