Zero-Dependent Bivariate Poisson Distribution with Applications
The bivariate Poisson model is the most widely used model for bivariate counts, and in recent years, several bivariate Poisson regression models have been developed in order to analyse two response variables that are possibly correlated. In this paper, a particular class of bivariate Poisson model,...
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| Format: | Article |
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MDPI AG
2023-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/5/1194 |
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| author | Najla Qarmalah Abdulhamid A. Alzaid |
| author_facet | Najla Qarmalah Abdulhamid A. Alzaid |
| author_sort | Najla Qarmalah |
| collection | DOAJ |
| description | The bivariate Poisson model is the most widely used model for bivariate counts, and in recent years, several bivariate Poisson regression models have been developed in order to analyse two response variables that are possibly correlated. In this paper, a particular class of bivariate Poisson model, developed from the bivariate Bernoulli model, will be presented and investigated. The proposed bivariate Poisson models use dependence parameters that can model positively and negatively correlated data, whereas more well-known models, such as Holgate’s bivariate Poisson model, can only be used for positively correlated data. As a result, the proposed model contributes to improving the properties of the more common bivariate Poisson regression models. Furthermore, some of the properties of the new bivariate Poisson model are outlined. The method of maximum likelihood and moment method were used to estimate the parameters of the proposed model. Additionally, real data from the healthcare utilization sector were used. As in the case of healthcare utilization, dependence between the two variables may be positive or negative in order to assess the performance of the proposed model, in comparison to traditional bivariate count models. All computations and graphs shown in this paper were produced using R programming language. |
| first_indexed | 2024-03-11T07:17:14Z |
| format | Article |
| id | doaj.art-0ae484c5fbd84dc4b0a1c62ac217daef |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T07:17:14Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-0ae484c5fbd84dc4b0a1c62ac217daef2023-11-17T08:09:30ZengMDPI AGMathematics2227-73902023-02-01115119410.3390/math11051194Zero-Dependent Bivariate Poisson Distribution with ApplicationsNajla Qarmalah0Abdulhamid A. Alzaid1Department of Mathematical Sciences, Princess Nourah bint Abdulrahman University, Riyadh 84428, Saudi ArabiaDepartment of Statistics and Operations Research, King Saud University, Riyadh 145111, Saudi ArabiaThe bivariate Poisson model is the most widely used model for bivariate counts, and in recent years, several bivariate Poisson regression models have been developed in order to analyse two response variables that are possibly correlated. In this paper, a particular class of bivariate Poisson model, developed from the bivariate Bernoulli model, will be presented and investigated. The proposed bivariate Poisson models use dependence parameters that can model positively and negatively correlated data, whereas more well-known models, such as Holgate’s bivariate Poisson model, can only be used for positively correlated data. As a result, the proposed model contributes to improving the properties of the more common bivariate Poisson regression models. Furthermore, some of the properties of the new bivariate Poisson model are outlined. The method of maximum likelihood and moment method were used to estimate the parameters of the proposed model. Additionally, real data from the healthcare utilization sector were used. As in the case of healthcare utilization, dependence between the two variables may be positive or negative in order to assess the performance of the proposed model, in comparison to traditional bivariate count models. All computations and graphs shown in this paper were produced using R programming language.https://www.mdpi.com/2227-7390/11/5/1194PoissonBernoullicount datamaximum likelihoodmoment methodregression |
| spellingShingle | Najla Qarmalah Abdulhamid A. Alzaid Zero-Dependent Bivariate Poisson Distribution with Applications Mathematics Poisson Bernoulli count data maximum likelihood moment method regression |
| title | Zero-Dependent Bivariate Poisson Distribution with Applications |
| title_full | Zero-Dependent Bivariate Poisson Distribution with Applications |
| title_fullStr | Zero-Dependent Bivariate Poisson Distribution with Applications |
| title_full_unstemmed | Zero-Dependent Bivariate Poisson Distribution with Applications |
| title_short | Zero-Dependent Bivariate Poisson Distribution with Applications |
| title_sort | zero dependent bivariate poisson distribution with applications |
| topic | Poisson Bernoulli count data maximum likelihood moment method regression |
| url | https://www.mdpi.com/2227-7390/11/5/1194 |
| work_keys_str_mv | AT najlaqarmalah zerodependentbivariatepoissondistributionwithapplications AT abdulhamidaalzaid zerodependentbivariatepoissondistributionwithapplications |