Bivariate Poisson 2Sum-Lindley Distributions and the Associated BINAR(1) Processes
Discrete-valued time series modeling has witnessed numerous bivariate first-order integer-valued autoregressive process or BINAR(1) processes based on binomial thinning and different innovation distributions. These BINAR(1) processes are mainly focused on over-dispersion. This paper aims to propose...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-10-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/20/3835 |
| _version_ | 1797431473753554944 |
|---|---|
| author | Muhammed Rasheed Irshad Christophe Chesneau Veena D’cruz Naushad Mamode Khan Radhakumari Maya |
| author_facet | Muhammed Rasheed Irshad Christophe Chesneau Veena D’cruz Naushad Mamode Khan Radhakumari Maya |
| author_sort | Muhammed Rasheed Irshad |
| collection | DOAJ |
| description | Discrete-valued time series modeling has witnessed numerous bivariate first-order integer-valued autoregressive process or BINAR(1) processes based on binomial thinning and different innovation distributions. These BINAR(1) processes are mainly focused on over-dispersion. This paper aims to propose new bivariate distributions and processes based on a recently proposed over-dispersed distribution: the Poisson 2S-Lindley distribution. The new bivariate distributions, denoted by the abbreviations BP2S-L(I) and BP2S-L(II), are then used as innovation distributions for the BINAR(1) process. Properties are investigated for both distributions as well as for the BINAR(1) processes. The distribution parameters are estimated using the maximum likelihood method, and the BINAR(1)BP2S-L(I) and BINAR(1)BP2S-L(II) process parameters are estimated using the conditional least squares and conditional maximum likelihood methods. Monte Carlo simulation experiments are conducted to study large and small sample performances and for the comparison of the estimation methods. The Pittsburgh crime series and candy sales datasets are then used to compare the new BINAR(1) processes to some other existing BINAR(1) processes in the literature. |
| first_indexed | 2024-03-09T09:45:35Z |
| format | Article |
| id | doaj.art-321e587b0d59445c9c7fbb8716bece80 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T09:45:35Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-321e587b0d59445c9c7fbb8716bece802023-12-02T00:36:05ZengMDPI AGMathematics2227-73902022-10-011020383510.3390/math10203835Bivariate Poisson 2Sum-Lindley Distributions and the Associated BINAR(1) ProcessesMuhammed Rasheed Irshad0Christophe Chesneau1Veena D’cruz2Naushad Mamode Khan3Radhakumari Maya4Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, IndiaDepartment of Mathematics (LMNO), University of Caen-Normandie, UFR de Sciences, F-14032 Caen, FranceDepartment of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, IndiaDepartment of Economics and Statistics, University of Mauritius, Réduit 80837, MauritiusDepartment of Statistics, University College, Trivandrum 695 014, Kerala, IndiaDiscrete-valued time series modeling has witnessed numerous bivariate first-order integer-valued autoregressive process or BINAR(1) processes based on binomial thinning and different innovation distributions. These BINAR(1) processes are mainly focused on over-dispersion. This paper aims to propose new bivariate distributions and processes based on a recently proposed over-dispersed distribution: the Poisson 2S-Lindley distribution. The new bivariate distributions, denoted by the abbreviations BP2S-L(I) and BP2S-L(II), are then used as innovation distributions for the BINAR(1) process. Properties are investigated for both distributions as well as for the BINAR(1) processes. The distribution parameters are estimated using the maximum likelihood method, and the BINAR(1)BP2S-L(I) and BINAR(1)BP2S-L(II) process parameters are estimated using the conditional least squares and conditional maximum likelihood methods. Monte Carlo simulation experiments are conducted to study large and small sample performances and for the comparison of the estimation methods. The Pittsburgh crime series and candy sales datasets are then used to compare the new BINAR(1) processes to some other existing BINAR(1) processes in the literature.https://www.mdpi.com/2227-7390/10/20/3835Poisson 2S-Lindley distributionbinomial thinningover-dispersionmomentsmaximum likelihood estimationsimulation |
| spellingShingle | Muhammed Rasheed Irshad Christophe Chesneau Veena D’cruz Naushad Mamode Khan Radhakumari Maya Bivariate Poisson 2Sum-Lindley Distributions and the Associated BINAR(1) Processes Mathematics Poisson 2S-Lindley distribution binomial thinning over-dispersion moments maximum likelihood estimation simulation |
| title | Bivariate Poisson 2Sum-Lindley Distributions and the Associated BINAR(1) Processes |
| title_full | Bivariate Poisson 2Sum-Lindley Distributions and the Associated BINAR(1) Processes |
| title_fullStr | Bivariate Poisson 2Sum-Lindley Distributions and the Associated BINAR(1) Processes |
| title_full_unstemmed | Bivariate Poisson 2Sum-Lindley Distributions and the Associated BINAR(1) Processes |
| title_short | Bivariate Poisson 2Sum-Lindley Distributions and the Associated BINAR(1) Processes |
| title_sort | bivariate poisson 2sum lindley distributions and the associated binar 1 processes |
| topic | Poisson 2S-Lindley distribution binomial thinning over-dispersion moments maximum likelihood estimation simulation |
| url | https://www.mdpi.com/2227-7390/10/20/3835 |
| work_keys_str_mv | AT muhammedrasheedirshad bivariatepoisson2sumlindleydistributionsandtheassociatedbinar1processes AT christophechesneau bivariatepoisson2sumlindleydistributionsandtheassociatedbinar1processes AT veenadcruz bivariatepoisson2sumlindleydistributionsandtheassociatedbinar1processes AT naushadmamodekhan bivariatepoisson2sumlindleydistributionsandtheassociatedbinar1processes AT radhakumarimaya bivariatepoisson2sumlindleydistributionsandtheassociatedbinar1processes |