Kharrati-Kopaei, Mahmood; Faghih, Havva Inferences for the inflation parameter in the ZIP distributions: the method of moments. (English) Zbl 1215.62022 Stat. Methodol. 8, No. 4, 377-388 (2011). Summary: The zero-inflated Poisson (ZIP) distribution is widely used for modeling a count data set when the frequency of zeros is higher than the one expected under the Poisson distribution. There are many methods for making inferences for the inflation parameter in the ZIP models, e.g. the methods for testing Poisson (the inflation parameter is zero) versus ZIP distributions (the inflation parameter is positive). Most of these methods are based on the maximum likelihood estimators which do not have an explicit expression. However, the estimators which are obtained by the method of moments are powerful enough, easy to obtain and implement. We propose an approach based on the method of moments for making inferences about the inflation parameter in the ZIP distribution. Our method is also compared to some recent methods via a simulation study and is illustrated by an example. Cited in 1 Document MSC: 62F10 Point estimation 62F25 Parametric tolerance and confidence regions 62E15 Exact distribution theory in statistics 65C60 Computational problems in statistics (MSC2010) Keywords:confidence interval; MME; Poisson; zero inflation PDFBibTeX XMLCite \textit{M. Kharrati-Kopaei} and \textit{H. Faghih}, Stat. Methodol. 8, No. 4, 377--388 (2011; Zbl 1215.62022) Full Text: DOI References: [1] Baillo, A.; Berrendero, J. R.; Carcamo, J., Tests for zero-inflation and overdispersion: a new approach based on the stochastic convex order, Computational Statistics and Data Analysis, 53, 2628-2639 (2009) · Zbl 1453.62034 [2] Bohning, D., A note on a test for Poisson overdispersion, Biometrika, 81, 418-419 (1994) · Zbl 0825.62459 [3] Boos, D.; Stefanski, L. A., The calculus of \(M\) estimation, The American Statistician, 56, 29-38 (2002) [4] Cochran, W. 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