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A new two-parameter discrete poisson-generalized Lindley distribution with properties and applications to healthcare data sets

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  • Emrah Altun

    (Bartin University)

Abstract

Mixed-Poisson distributions have been used in many fields for modeling the over-dispersed count data sets. To open a new opportunity in modeling the over-dispersed count data sets, we introduce a new mixed-Poisson distribution using the generalized Lindley distribution as a mixing distribution. The moment and probability generating functions, factorial moments as well as skewness, and kurtosis measures are derived. Using the mean-parametrized version of the proposed distribution, we introduce a new count regression model which is an appropriate model for over-dispersed counts. The healthcare data sets are analyzed employing a new count regression model. We conclude that the new regression model works well in the case of over-dispersion.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:4:d:10.1007_s00180-021-01097-0
    DOI: 10.1007/s00180-021-01097-0
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    References listed on IDEAS

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    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. Weerinrada Wongrin & Winai Bodhisuwan, 2017. "Generalized Poisson–Lindley linear model for count data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(15), pages 2659-2671, November.
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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. Mohanan Monisha & Damodaran Santhamani Shibu, 2024. "On Discrete Mixture of Moment Exponential Using Lagrangian Probability Model: Properties and Applications in Count Data with Excess Zeros," Annals of Data Science, Springer, vol. 11(6), pages 2035-2057, 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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