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A new count model generated from mixed Poisson transmuted exponential family with an application to health care data

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  • Deepesh Bhati
  • Pooja Kumawat
  • E. Gómez–Déniz

Abstract

In this article, a new mixed Poisson distribution is introduced. This new distribution is obtained by utilizing mixing process, with Poisson distribution as mixed distribution and Transmuted Exponential as mixing distribution. Distributional properties like unimodality, moments, over-dispersion, infinite divisibility are studied. Three methods viz. Method of moment, Method of moment and proportion, and Maximum-likelihood method are used for parameter estimation. Further, an actuarial application in context of aggregate claim distribution is presented. Finally, to show the applicability and superiority of proposed model, we discuss count data and count regression modeling and compare with some well established models.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:22:p:11060-11076
    DOI: 10.1080/03610926.2016.1257712
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Sima Ghazanfari & Ali Firoozzare & Daniela Covino & Flavio Boccia & Nadia Palmieri, 2024. "Exploring Factors Influencing Consumers’ Willingness to Pay Healthy-Labeled Foods at a Premium Price," Sustainability, MDPI, vol. 16(16), pages 1-21, August.
    5. 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.

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