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Modeling data with a truncated and inflated Poisson distribution

Author

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  • Min-Hsiao Tsai

    (National Taipei University)

  • Ting Hsiang Lin

    (National Taipei University)

Abstract

Zero inflated Poisson regression is a model commonly used to analyze data with excessive zeros. Although many models have been developed to fit zero-inflated data, most of them strongly depend on the special features of the individual data. For example, there is a need for new models when dealing with truncated and inflated data. In this paper, we propose a new model that is sufficiently flexible to model inflation and truncation simultaneously, and which is a mixture of a multinomial logistic and a truncated Poisson regression, in which the multinomial logistic component models the occurrence of excessive counts. The truncated Poisson regression models the counts that are assumed to follow a truncated Poisson distribution. The performance of our proposed model is evaluated through simulation studies, and our model is found to have the smallest mean absolute error and best model fit. In the empirical example, the data are truncated with inflated values of zero and fourteen, and the results show that our model has a better fit than the other competing models.

Suggested Citation

  • Min-Hsiao Tsai & Ting Hsiang Lin, 2017. "Modeling data with a truncated and inflated Poisson distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(3), pages 383-401, August.
    • Handle: RePEc:spr:stmapp:v:26:y:2017:i:3:d:10.1007_s10260-017-0377-z
    DOI: 10.1007/s10260-017-0377-z
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    References listed on IDEAS

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    1. Bae, S. & Famoye, F. & Wulu, J.T. & Bartolucci, A.A. & Singh, K.P., 2005. "A rich family of generalized Poisson regression models with applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 69(1), pages 4-11.
    2. Zhou Xiao-Hua & Wanzhu Tu, 1999. "Comparison of Several Independent Population Means When Their Samples Contain Log-Normal and Possibly Zero Observations," Biometrics, The International Biometric Society, vol. 55(2), pages 645-651, June.
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