A New Double Truncated Generalized Gamma Model with Some Applications
The generalized Gamma model has been applied in a variety of research fields, including reliability engineering and lifetime analysis. Indeed, we know that, from the above, it is unbounded. Data have a bounded service area in a variety of applications. A new five-parameter bounded generalized Gamma...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5500631 |
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| author | Awad A. Bakery Wael Zakaria OM Kalthum S. K. Mohamed |
| author_facet | Awad A. Bakery Wael Zakaria OM Kalthum S. K. Mohamed |
| author_sort | Awad A. Bakery |
| collection | DOAJ |
| description | The generalized Gamma model has been applied in a variety of research fields, including reliability engineering and lifetime analysis. Indeed, we know that, from the above, it is unbounded. Data have a bounded service area in a variety of applications. A new five-parameter bounded generalized Gamma model, the bounded Weibull model with four parameters, the bounded Gamma model with four parameters, the bounded generalized Gaussian model with three parameters, the bounded exponential model with three parameters, and the bounded Rayleigh model with two parameters, is presented in this paper as a special case. This approach to the problem, which utilizes a bounded support area, allows for a great deal of versatility in fitting various shapes of observed data. Numerous properties of the proposed distribution have been deduced, including explicit expressions for the moments, quantiles, mode, moment generating function, mean variance, mean residual lifespan, and entropies, skewness, kurtosis, hazard function, survival function, r th order statistic, and median distributions. The delivery has hazard frequencies that are monotonically increasing or declining, bathtub-shaped, or upside-down bathtub-shaped. We use the Newton Raphson approach to approximate model parameters that increase the log-likelihood function and some of the parameters have a closed iterative structure. Six actual data sets and six simulated data sets were tested to demonstrate how the proposed model works in reality. We illustrate why the Model is more stable and less affected by sample size. Additionally, the suggested model for wavelet histogram fitting of images and sounds is very accurate. |
| format | Article |
| id | doaj-art-fc8d2571ac8d4bfc9c76180b7cc2cb8d |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-fc8d2571ac8d4bfc9c76180b7cc2cb8d2025-02-03T01:27:21ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55006315500631A New Double Truncated Generalized Gamma Model with Some ApplicationsAwad A. Bakery0Wael Zakaria1OM Kalthum S. K. Mohamed2University of Jeddah, College of Science and Arts at Khulis, Department of Mathematics, Jeddah, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Ain Shams University, P.O. Box 1156, Abbassia, Cairo 11566, EgyptUniversity of Jeddah, College of Science and Arts at Khulis, Department of Mathematics, Jeddah, Saudi ArabiaThe generalized Gamma model has been applied in a variety of research fields, including reliability engineering and lifetime analysis. Indeed, we know that, from the above, it is unbounded. Data have a bounded service area in a variety of applications. A new five-parameter bounded generalized Gamma model, the bounded Weibull model with four parameters, the bounded Gamma model with four parameters, the bounded generalized Gaussian model with three parameters, the bounded exponential model with three parameters, and the bounded Rayleigh model with two parameters, is presented in this paper as a special case. This approach to the problem, which utilizes a bounded support area, allows for a great deal of versatility in fitting various shapes of observed data. Numerous properties of the proposed distribution have been deduced, including explicit expressions for the moments, quantiles, mode, moment generating function, mean variance, mean residual lifespan, and entropies, skewness, kurtosis, hazard function, survival function, r th order statistic, and median distributions. The delivery has hazard frequencies that are monotonically increasing or declining, bathtub-shaped, or upside-down bathtub-shaped. We use the Newton Raphson approach to approximate model parameters that increase the log-likelihood function and some of the parameters have a closed iterative structure. Six actual data sets and six simulated data sets were tested to demonstrate how the proposed model works in reality. We illustrate why the Model is more stable and less affected by sample size. Additionally, the suggested model for wavelet histogram fitting of images and sounds is very accurate.http://dx.doi.org/10.1155/2021/5500631 |
| spellingShingle | Awad A. Bakery Wael Zakaria OM Kalthum S. K. Mohamed A New Double Truncated Generalized Gamma Model with Some Applications Journal of Mathematics |
| title | A New Double Truncated Generalized Gamma Model with Some Applications |
| title_full | A New Double Truncated Generalized Gamma Model with Some Applications |
| title_fullStr | A New Double Truncated Generalized Gamma Model with Some Applications |
| title_full_unstemmed | A New Double Truncated Generalized Gamma Model with Some Applications |
| title_short | A New Double Truncated Generalized Gamma Model with Some Applications |
| title_sort | new double truncated generalized gamma model with some applications |
| url | http://dx.doi.org/10.1155/2021/5500631 |
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