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New One-Parameter Over-Dispersed Discrete Distribution and Its Application to the Nonnegative Integer-Valued Autoregressive Model of Order One

Author

Listed:
  • Muhammed Rasheed Irshad

    (Department of Statistics, Cochin University of Science and Technology, Cochin 682022, India)

  • Sreedeviamma Aswathy

    (Department of Statistics, Cochin University of Science and Technology, Cochin 682022, India)

  • Radhakumari Maya

    (Department of Statistics, University College, Thiruvananthapuram 695034, India)

  • Saralees Nadarajah

    (Department of Mathematics, University of Manchester, Manchester M13 9PL, UK)

Abstract

Count data arise in inference, modeling, prediction, anomaly detection, monitoring, resource allocation, evaluation, and performance measurement. This paper focuses on a one-parameter discrete distribution obtained by compounding the Poisson and new X-Lindley distributions. The probability-generating function, moments, skewness, kurtosis, and other properties are derived in the closed form. The maximum likelihood method, method of moments, least squares method, and weighted least squares method are used for parameter estimation. A simulation study is carried out. The proposed distribution is applied as the innovation in an INAR(1) process. The importance of the proposed model is confirmed through the analysis of two real datasets.

Suggested Citation

  • Muhammed Rasheed Irshad & Sreedeviamma Aswathy & Radhakumari Maya & Saralees Nadarajah, 2023. "New One-Parameter Over-Dispersed Discrete Distribution and Its Application to the Nonnegative Integer-Valued Autoregressive Model of Order One," Mathematics, MDPI, vol. 12(1), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:81-:d:1307745
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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. Kimberly F. Sellers & Sharad Borle & Galit Shmueli, 2012. "The COM‐Poisson model for count data: a survey of methods and applications," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 28(2), pages 104-116, March.
    3. 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.
    4. 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.
    5. 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.
    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.
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