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Poisson Extended Exponential Distribution with Associated INAR(1) Process and Applications

Author

Listed:
  • Radhakumari Maya

    (Department of Statistics, Government College for Women, Trivandrum 695 014, Kerala, India)

  • Christophe Chesneau

    (Department of Mathematics, Université de Caen Basse-Normandie, F-14032 Caen, France)

  • Anuresha Krishna

    (Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India)

  • Muhammed Rasheed Irshad

    (Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India)

Abstract

The significance of count data modeling and its applications to real-world phenomena have been highlighted in several research studies. The present study focuses on a two-parameter discrete distribution that can be obtained by compounding the Poisson and extended exponential distributions. It has tractable and explicit forms for its statistical properties. The maximum likelihood estimation method is used to estimate the unknown parameters. An extensive simulation study was also performed. In this paper, the significance of the proposed distribution is demonstrated in a count regression model and in a first-order integer-valued autoregressive process, referred to as the INAR(1) process. In addition to this, the empirical importance of the proposed model is proved through three real-data applications, and the empirical findings indicate that the proposed INAR(1) model provides better results than other competitive models for time series of counts that display overdispersion.

Suggested Citation

  • Radhakumari Maya & Christophe Chesneau & Anuresha Krishna & Muhammed Rasheed Irshad, 2022. "Poisson Extended Exponential Distribution with Associated INAR(1) Process and Applications," Stats, MDPI, vol. 5(3), pages 1-18, August.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:3:p:44-772:d:881002
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    References listed on IDEAS

    as
    1. Deepesh Bhati & Pooja Kumawat & E. Gómez–Déniz, 2017. "A new count model generated from mixed Poisson transmuted exponential family with an application to health care data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(22), pages 11060-11076, November.
    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. 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.
    4. Emrah Altun, 2021. "A new two-parameter discrete poisson-generalized Lindley distribution with properties and applications to healthcare data sets," Computational Statistics, Springer, vol. 36(4), pages 2841-2861, December.
    5. M. El-Morshedy & M. S. Eliwa & H. Nagy, 2020. "A new two-parameter exponentiated discrete Lindley distribution: properties, estimation and applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(2), pages 354-375, January.
    6. Emrah Altun & Naushad Mamode Khan, 2022. "Modelling with the Novel INAR(1)-PTE Process," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1735-1751, September.
    7. M. A. Al‐Osh & A. A. Alzaid, 1987. "First‐Order Integer‐Valued Autoregressive (Inar(1)) Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(3), pages 261-275, May.
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