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Article

On Discrete Poisson–Mirra Distribution: Regression, INAR(1) Process and Applications

by
Radhakumari Maya
1,
Muhammed Rasheed Irshad
2,
Christophe Chesneau
3,*,
Soman Latha Nitin
4 and
Damodaran Santhamani Shibu
4
1
Department of Statistics, Government College for Women, Thiruvananthapuram 695 014, Kerala, India
2
Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India
3
Department of Mathematics, Université de Caen Basse-Normandie, LMNO, UFR de Sciences, F-14032 Caen, France
4
Department of Statistics, University College, Thiruvananthapuram 695 034, Kerala, India
*
Author to whom correspondence should be addressed.
Axioms 2022, 11(5), 193; https://doi.org/10.3390/axioms11050193
Submission received: 28 March 2022 / Revised: 17 April 2022 / Accepted: 20 April 2022 / Published: 21 April 2022
(This article belongs to the Special Issue Advances in Applied Mathematical Modelling)
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Abstract

Several pieces of research have spotlighted the importance of count data modelling and its applications in real-world phenomena. In light of this, a novel two-parameter compound-Poisson distribution is developed in this paper. Its mathematical functionalities are investigated. The two unknown parameters are estimated using both maximum likelihood and Bayesian approaches. We also offer a parametric regression model for the count datasets based on the proposed distribution. Furthermore, the first-order integer-valued autoregressive process, or INAR(1) process, is also used to demonstrate the utility of the suggested distribution in time series analysis. The unknown parameters of the proposed INAR(1) model are estimated using the conditional maximum likelihood, conditional least squares, and Yule–Walker techniques. Simulation studies for the suggested distribution and the INAR(1) model based on this innovative distribution are also undertaken as an assessment of the long-term performance of the estimators. Finally, we utilized three real datasets to depict the new model’s real-world applicability.
Keywords: compounding; over-dispersion; Bayesian estimation; count time series; COVID-19 data; earthquake data compounding; over-dispersion; Bayesian estimation; count time series; COVID-19 data; earthquake data

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MDPI and ACS Style

Maya, R.; Irshad, M.R.; Chesneau, C.; Nitin, S.L.; Shibu, D.S. On Discrete Poisson–Mirra Distribution: Regression, INAR(1) Process and Applications. Axioms 2022, 11, 193. https://doi.org/10.3390/axioms11050193

AMA Style

Maya R, Irshad MR, Chesneau C, Nitin SL, Shibu DS. On Discrete Poisson–Mirra Distribution: Regression, INAR(1) Process and Applications. Axioms. 2022; 11(5):193. https://doi.org/10.3390/axioms11050193

Chicago/Turabian Style

Maya, Radhakumari, Muhammed Rasheed Irshad, Christophe Chesneau, Soman Latha Nitin, and Damodaran Santhamani Shibu. 2022. "On Discrete Poisson–Mirra Distribution: Regression, INAR(1) Process and Applications" Axioms 11, no. 5: 193. https://doi.org/10.3390/axioms11050193

APA Style

Maya, R., Irshad, M. R., Chesneau, C., Nitin, S. L., & Shibu, D. S. (2022). On Discrete Poisson–Mirra Distribution: Regression, INAR(1) Process and Applications. Axioms, 11(5), 193. https://doi.org/10.3390/axioms11050193

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