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On inflated generalized Poisson regression models. (English) Zbl 1042.62063

Summary: Zero-inflated Poisson and zero-inflated negative binomial regression models have been proposed for data sets that result into too many zeros. Recently, the zero-inflated generalized Poisson regression model is defined as a good alternate to model count data with too many zeros [the authors, Zero inflated generalized Poisson regression model. submitted]. In this paper, we propose a \(k\)-inflated generalized Poisson regression to model count data with too many \(k\)-values.
Estimation of the model parameters using the method of maximum likelihood is provided. A score test is presented to test whether the number of \(k\)-values is too large for the generalized Poisson model to adequately fit the data. The \(k\)-inflated generalized Poisson regression model is illustrated using a dataset with too many ones.

MSC:

62J02 General nonlinear regression
62F10 Point estimation
62J12 Generalized linear models (logistic models)
62P10 Applications of statistics to biology and medical sciences; meta analysis
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