A Novel Flexible Class of Intervened Poisson Distribution by Lagrangian Approach
The zero-truncated Poisson distribution (ZTPD) generates a statistical model that could be appropriate when observations begin once at least one event occurs. The intervened Poisson distribution (IPD) is a substitute for the ZTPD, in which some intervention processes may change the mean of the rare...
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MDPI AG
2023-01-01
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| author | Muhammed Rasheed Irshad Mohanan Monisha Christophe Chesneau Radhakumari Maya Damodaran Santhamani Shibu |
| author_facet | Muhammed Rasheed Irshad Mohanan Monisha Christophe Chesneau Radhakumari Maya Damodaran Santhamani Shibu |
| author_sort | Muhammed Rasheed Irshad |
| collection | DOAJ |
| description | The zero-truncated Poisson distribution (ZTPD) generates a statistical model that could be appropriate when observations begin once at least one event occurs. The intervened Poisson distribution (IPD) is a substitute for the ZTPD, in which some intervention processes may change the mean of the rare events. These two zero-truncated distributions exhibit underdispersion (i.e., their variance is less than their mean). In this research, we offer an alternative solution for dealing with intervention problems by proposing a generalization of the IPD by a Lagrangian approach called the Lagrangian intervened Poisson distribution (LIPD), which in fact generalizes both the ZTPD and the IPD. As a notable feature, it has the ability to analyze both overdispersed and underdispersed datasets. In addition, the LIPD has a closed-form expression of all of its statistical characteristics, as well as an increasing, decreasing, bathtub-shaped, and upside-down bathtub-shaped hazard rate function. A consequent part is devoted to its statistical application. The maximum likelihood estimation method is considered, and the effectiveness of the estimates is demonstrated through a simulated study. To evaluate the significance of the new parameter in the LIPD, a generalized likelihood ratio test is performed. Subsequently, we present a new count regression model that is suitable for both overdispersed and underdispersed datasets using the mean-parametrized form of the LIPD. Additionally, the LIPD’s relevance and application are shown using real-world datasets. |
| first_indexed | 2024-03-11T05:54:02Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2571-905X |
| language | English |
| last_indexed | 2024-03-11T05:54:02Z |
| publishDate | 2023-01-01 |
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| series | Stats |
| spelling | doaj.art-1781225c25b143e591a0a3f3fe73f31b2023-11-17T13:53:51ZengMDPI AGStats2571-905X2023-01-016115016810.3390/stats6010010A Novel Flexible Class of Intervened Poisson Distribution by Lagrangian ApproachMuhammed Rasheed Irshad0Mohanan Monisha1Christophe Chesneau2Radhakumari Maya3Damodaran Santhamani Shibu4Department of Statistics, Cochin University of Science and Technology, Cochin 682022, IndiaDepartment of Statistics, University College, Thiruvananthapuram 695034, IndiaDepartment of Mathematics, Université de Caen Basse-Normandie, UFR de Sciences, 14032 Caen, FranceDepartment of Statistics, University College, Thiruvananthapuram 695034, IndiaDepartment of Statistics, University College, Thiruvananthapuram 695034, IndiaThe zero-truncated Poisson distribution (ZTPD) generates a statistical model that could be appropriate when observations begin once at least one event occurs. The intervened Poisson distribution (IPD) is a substitute for the ZTPD, in which some intervention processes may change the mean of the rare events. These two zero-truncated distributions exhibit underdispersion (i.e., their variance is less than their mean). In this research, we offer an alternative solution for dealing with intervention problems by proposing a generalization of the IPD by a Lagrangian approach called the Lagrangian intervened Poisson distribution (LIPD), which in fact generalizes both the ZTPD and the IPD. As a notable feature, it has the ability to analyze both overdispersed and underdispersed datasets. In addition, the LIPD has a closed-form expression of all of its statistical characteristics, as well as an increasing, decreasing, bathtub-shaped, and upside-down bathtub-shaped hazard rate function. A consequent part is devoted to its statistical application. The maximum likelihood estimation method is considered, and the effectiveness of the estimates is demonstrated through a simulated study. To evaluate the significance of the new parameter in the LIPD, a generalized likelihood ratio test is performed. Subsequently, we present a new count regression model that is suitable for both overdispersed and underdispersed datasets using the mean-parametrized form of the LIPD. Additionally, the LIPD’s relevance and application are shown using real-world datasets.https://www.mdpi.com/2571-905X/6/1/10Lagrange expansionintervened Poisson distributionLagrangian intervened Poisson distributionregressioninverse transformation method |
| spellingShingle | Muhammed Rasheed Irshad Mohanan Monisha Christophe Chesneau Radhakumari Maya Damodaran Santhamani Shibu A Novel Flexible Class of Intervened Poisson Distribution by Lagrangian Approach Stats Lagrange expansion intervened Poisson distribution Lagrangian intervened Poisson distribution regression inverse transformation method |
| title | A Novel Flexible Class of Intervened Poisson Distribution by Lagrangian Approach |
| title_full | A Novel Flexible Class of Intervened Poisson Distribution by Lagrangian Approach |
| title_fullStr | A Novel Flexible Class of Intervened Poisson Distribution by Lagrangian Approach |
| title_full_unstemmed | A Novel Flexible Class of Intervened Poisson Distribution by Lagrangian Approach |
| title_short | A Novel Flexible Class of Intervened Poisson Distribution by Lagrangian Approach |
| title_sort | novel flexible class of intervened poisson distribution by lagrangian approach |
| topic | Lagrange expansion intervened Poisson distribution Lagrangian intervened Poisson distribution regression inverse transformation method |
| url | https://www.mdpi.com/2571-905X/6/1/10 |
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