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On Poisson Moment Exponential Distribution with Associated Regression and INAR(1) Process

Author

Listed:
  • R. Maya

    (University College)

  • Jie Huang

    (Chang’an University)

  • M. R. Irshad

    (Cochin University of Science and Technology)

  • Fukang Zhu

    (Jilin University)

Abstract

Numerous studies have emphasised the significance of count data modeling and its applications to phenomena that occur in the real world. From this perspective, this article examines the traits and applications of the Poisson-moment exponential (PME) distribution in the contexts of time series analysis and regression analysis for real-world phenomena. The PME distribution is a novel one-parameter discrete distribution that can be used as a powerful alternative for the existing distributions for modeling over-dispersed count datasets. The advantages of the PME distribution, including the simplicity of the probability mass function and the explicit expressions of the functions of all the statistical properties, drove us to develop the inferential aspects and learn more about its practical applications. The unknown parameter is estimated using both maximum likelihood and moment estimation methods. Also, we present a parametric regression model based on the PME distribution for the count datasets. To strengthen the utility of the suggested distribution, we propose a new first-order integer-valued autoregressive (INAR(1)) process with PME innovations based on binomial thinning for modeling integer-valued time series with over-dispersion. Application to four real datasets confirms the empirical significance of the proposed model.

Suggested Citation

  • R. Maya & Jie Huang & M. R. Irshad & Fukang Zhu, 2024. "On Poisson Moment Exponential Distribution with Associated Regression and INAR(1) Process," Annals of Data Science, Springer, vol. 11(5), pages 1741-1759, October.
    • Handle: RePEc:spr:aodasc:v:11:y:2024:i:5:d:10.1007_s40745-023-00476-2
    DOI: 10.1007/s40745-023-00476-2
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    References listed on IDEAS

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    1. Rigby, R.A. & Stasinopoulos, D.M. & Akantziliotou, C., 2008. "A framework for modelling overdispersed count data, including the Poisson-shifted generalized inverse Gaussian distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 381-393, December.
    2. Emrah Altun & Gauss M. Cordeiro & Miroslav M. Ristić, 2022. "An one-parameter compounding discrete distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(8), pages 1935-1956, June.
    3. Mullahy, John, 1997. "Heterogeneity, Excess Zeros, and the Structure of Count Data Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(3), pages 337-350, May-June.
    4. Schweer, Sebastian & Weiß, Christian H., 2014. "Compound Poisson INAR(1) processes: Stochastic properties and testing for overdispersion," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 267-284.
    5. Tito Lívio & Naushad Mamode Khan & Marcelo Bourguignon & Hassan S. Bakouch, 2018. "An INAR(1) model with Poisson-Lindley innovations," Economics Bulletin, AccessEcon, vol. 38(3), pages 1505-1513.
    6. James M. Tien, 2017. "Internet of Things, Real-Time Decision Making, and Artificial Intelligence," Annals of Data Science, Springer, vol. 4(2), pages 149-178, June.
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