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An one-parameter compounding discrete distribution

Author

Listed:
  • Emrah Altun
  • Gauss M. Cordeiro
  • Miroslav M. Ristić

Abstract

In this study, a new one-parameter discrete distribution obtained by compounding the Poisson and xgamma distributions is proposed. Some statistical properties of the new distribution are obtained including moments and probability and moment generating functions. Two methods are used for the estimation of the unknown parameter: the maximum likelihood method and the method of moments. Additionally, the count regression model and integer-valued autoregressive process of the proposed distribution are introduced. Some possible applications of the introduced models are considered and discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:49:y:2022:i:8:p:1935-1956
    DOI: 10.1080/02664763.2021.1884846
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    Cited by:

    1. 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.
    2. 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.
    3. Ané van der Merwe & Johannes T. Ferreira, 2022. "An Adapted Discrete Lindley Model Emanating from Negative Binomial Mixtures for Autoregressive Counts," Mathematics, MDPI, vol. 10(21), pages 1-21, November.

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