Forecasting New Product Diffusion Using Grey Time-Delayed Verhulst Model
Taking account of the time-delayed phenomenon in diffusion of new products, we propose the time-delayed Verhulst model and then establish a grey time-delayed Verhulst model using the method of grey differential equations. The related parameter packets of this novel model are obtained under the rule...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/625028 |
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| _version_ | 1832549655350607872 |
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| author | Yuhong Wang Shulin Yang Wuyong Qian Xiaozhong Li |
| author_facet | Yuhong Wang Shulin Yang Wuyong Qian Xiaozhong Li |
| author_sort | Yuhong Wang |
| collection | DOAJ |
| description | Taking account of the time-delayed phenomenon in diffusion of new products, we propose the time-delayed Verhulst model and then establish a grey time-delayed Verhulst model using the method of grey differential equations. The related parameter packets of this novel model are obtained under the rule of ordinary least squares (OLS). The results show that the traditional grey Verhulst model is a special example of grey time-delayed Verhulst model which can reflect the time-delayed information effectively. A practical example of market diffusion shows that the modeling accuracy is remarkably improved by using the grey time-delayed Verhulst model presented in this paper. |
| format | Article |
| id | doaj-art-614ab7d67aa44e67a278afefd36f360a |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-614ab7d67aa44e67a278afefd36f360a2025-02-03T06:10:48ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/625028625028Forecasting New Product Diffusion Using Grey Time-Delayed Verhulst ModelYuhong Wang0Shulin Yang1Wuyong Qian2Xiaozhong Li3School of Business, Jiangnan University, Wuxi 214122, ChinaSchool of Business, Jiangnan University, Wuxi 214122, ChinaSchool of Business, Jiangnan University, Wuxi 214122, ChinaSchool of Business, Jiangnan University, Wuxi 214122, ChinaTaking account of the time-delayed phenomenon in diffusion of new products, we propose the time-delayed Verhulst model and then establish a grey time-delayed Verhulst model using the method of grey differential equations. The related parameter packets of this novel model are obtained under the rule of ordinary least squares (OLS). The results show that the traditional grey Verhulst model is a special example of grey time-delayed Verhulst model which can reflect the time-delayed information effectively. A practical example of market diffusion shows that the modeling accuracy is remarkably improved by using the grey time-delayed Verhulst model presented in this paper.http://dx.doi.org/10.1155/2013/625028 |
| spellingShingle | Yuhong Wang Shulin Yang Wuyong Qian Xiaozhong Li Forecasting New Product Diffusion Using Grey Time-Delayed Verhulst Model Journal of Applied Mathematics |
| title | Forecasting New Product Diffusion Using Grey Time-Delayed Verhulst Model |
| title_full | Forecasting New Product Diffusion Using Grey Time-Delayed Verhulst Model |
| title_fullStr | Forecasting New Product Diffusion Using Grey Time-Delayed Verhulst Model |
| title_full_unstemmed | Forecasting New Product Diffusion Using Grey Time-Delayed Verhulst Model |
| title_short | Forecasting New Product Diffusion Using Grey Time-Delayed Verhulst Model |
| title_sort | forecasting new product diffusion using grey time delayed verhulst model |
| url | http://dx.doi.org/10.1155/2013/625028 |
| work_keys_str_mv | AT yuhongwang forecastingnewproductdiffusionusinggreytimedelayedverhulstmodel AT shulinyang forecastingnewproductdiffusionusinggreytimedelayedverhulstmodel AT wuyongqian forecastingnewproductdiffusionusinggreytimedelayedverhulstmodel AT xiaozhongli forecastingnewproductdiffusionusinggreytimedelayedverhulstmodel |