Lagrangian Zero Truncated Poisson Distribution: Properties Regression Model and Applications
In this paper, we construct a new Lagrangian discrete distribution, named the Lagrangian zero truncated Poisson distribution (LZTPD). It can be presented as a generalization of the zero truncated Poissson distribution (ZTPD) and an alternative to the intervened Poisson distribution (IPD), which was...
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| Format: | Article |
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MDPI AG
2022-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/9/1775 |
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| author | Muhammed Rasheed Irshad Christophe Chesneau Damodaran Santhamani Shibu Mohanan Monisha Radhakumari Maya |
| author_facet | Muhammed Rasheed Irshad Christophe Chesneau Damodaran Santhamani Shibu Mohanan Monisha Radhakumari Maya |
| author_sort | Muhammed Rasheed Irshad |
| collection | DOAJ |
| description | In this paper, we construct a new Lagrangian discrete distribution, named the Lagrangian zero truncated Poisson distribution (LZTPD). It can be presented as a generalization of the zero truncated Poissson distribution (ZTPD) and an alternative to the intervened Poisson distribution (IPD), which was elaborated for modelling both over-dispersed and under-dispersed count datasets. The mathematical aspects of the LZTPD are thoroughly investigated, and its connection to other discrete distributions is crucially observed. Further, we define a finite mixture of LZTPDs and establish its identifiability condition along with some distributional aspects. Statistical work is then performed. The maximum likelihood and method of moment approaches are used to estimate the unknown parameters of the LZTPD. Simulation studies are also undertaken as an assessment of the long-term performance of the estimates. The significance of one additional parameter in the LZTPD is tested using a generalized likelihood ratio test. Moreover, we propose a new count regression model named the Lagrangian zero truncated Poisson regression model (LZTPRM) and its parameters are estimated by the maximum likelihood estimation method. Two real-world datasets are considered to demonstrate the LZTPD’s real-world applicability, and healthcare data are analyzed to demonstrate the LZTPRM’s superiority. |
| first_indexed | 2024-03-09T22:23:26Z |
| format | Article |
| id | doaj.art-bed8f62798f74aa6b0426d4d96535934 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T22:23:26Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-bed8f62798f74aa6b0426d4d965359342023-11-23T19:10:45ZengMDPI AGSymmetry2073-89942022-08-01149177510.3390/sym14091775Lagrangian Zero Truncated Poisson Distribution: Properties Regression Model and ApplicationsMuhammed Rasheed Irshad0Christophe Chesneau1Damodaran Santhamani Shibu2Mohanan Monisha3Radhakumari Maya4Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, IndiaDepartment of Mathematics, Université de Caen Basse-Normandie, LMNO, UFR de Sciences, F-14032 Caen, FranceDepartment of Statistics, University College, Thiruvananthapuram 695 034, Kerala, IndiaDepartment of Statistics, University College, Thiruvananthapuram 695 034, Kerala, IndiaDepartment of Statistics, Government College for Women, Thiruvananthapuram 695 014, Kerala, IndiaIn this paper, we construct a new Lagrangian discrete distribution, named the Lagrangian zero truncated Poisson distribution (LZTPD). It can be presented as a generalization of the zero truncated Poissson distribution (ZTPD) and an alternative to the intervened Poisson distribution (IPD), which was elaborated for modelling both over-dispersed and under-dispersed count datasets. The mathematical aspects of the LZTPD are thoroughly investigated, and its connection to other discrete distributions is crucially observed. Further, we define a finite mixture of LZTPDs and establish its identifiability condition along with some distributional aspects. Statistical work is then performed. The maximum likelihood and method of moment approaches are used to estimate the unknown parameters of the LZTPD. Simulation studies are also undertaken as an assessment of the long-term performance of the estimates. The significance of one additional parameter in the LZTPD is tested using a generalized likelihood ratio test. Moreover, we propose a new count regression model named the Lagrangian zero truncated Poisson regression model (LZTPRM) and its parameters are estimated by the maximum likelihood estimation method. Two real-world datasets are considered to demonstrate the LZTPD’s real-world applicability, and healthcare data are analyzed to demonstrate the LZTPRM’s superiority.https://www.mdpi.com/2073-8994/14/9/1775Lagrangian zero truncated Poisson distributionintervened Poisson distributionindex of dispersionregressionmaximum likelihood estimationgeneralized likelihood ratio test |
| spellingShingle | Muhammed Rasheed Irshad Christophe Chesneau Damodaran Santhamani Shibu Mohanan Monisha Radhakumari Maya Lagrangian Zero Truncated Poisson Distribution: Properties Regression Model and Applications Symmetry Lagrangian zero truncated Poisson distribution intervened Poisson distribution index of dispersion regression maximum likelihood estimation generalized likelihood ratio test |
| title | Lagrangian Zero Truncated Poisson Distribution: Properties Regression Model and Applications |
| title_full | Lagrangian Zero Truncated Poisson Distribution: Properties Regression Model and Applications |
| title_fullStr | Lagrangian Zero Truncated Poisson Distribution: Properties Regression Model and Applications |
| title_full_unstemmed | Lagrangian Zero Truncated Poisson Distribution: Properties Regression Model and Applications |
| title_short | Lagrangian Zero Truncated Poisson Distribution: Properties Regression Model and Applications |
| title_sort | lagrangian zero truncated poisson distribution properties regression model and applications |
| topic | Lagrangian zero truncated Poisson distribution intervened Poisson distribution index of dispersion regression maximum likelihood estimation generalized likelihood ratio test |
| url | https://www.mdpi.com/2073-8994/14/9/1775 |
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