• The Korean Journal of Applied Statistics
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• v.28 no.2
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• pp.231-239
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• 2015

A Poisson model is the first choice for counts data. Quasi Poisson or negative binomial models are usually used in cases of over (or under) dispersed data. However, these models might be unsuitable if the data consist of excessive number of zeros (zero inflated data). For zero inflated counts data, Zero Inflated Poisson (ZIP) or Zero Inflated Negative Binomial (ZINB) models are recommended to address the issue. In this paper, we further considered a situation where zero inflated data are spatially correlated. A mixed effect model with random effects that account for spatial autocorrelation is used to fit the data.

• Journal of the Korean Data and Information Science Society
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• v.9 no.1
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• pp.1-9
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• 1998

In case of Zero-Inflated Poisson model with a change-point, likelihood ratio test statistic was used for testing hypothesis for a change-point. A change-point and several interesting parameters were estimated by using the method of moments and maximum likelihood. In order to compare the estimators, empirical mean-square-error was used. Real data for the Zero-Inflated Poisson model with a change-point and Poisson model without a change-point were examined.

• Journal of the Korean Data and Information Science Society
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• v.9 no.1
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• pp.47-56
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• 1998

Zero-Inflated Poisson models are mixed models of the Poisson and Bernoulli models. Recently Zero-Inflated Poisson distributions have been used frequently rather than previous Poisson distributions because the developement of industrial technology make few defects in manufacturing process. It is important that univariate Zero-Inflated Poisson distributions are extended to bivariate distributions to generalize the multivariate distributions. In this paper we proposed three types of the bivariate Zero-Inflated Poisson distributions and obtained these moments. We compared the three types of distributions by using the moments.

• Journal of the Korean Data and Information Science Society
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• v.10 no.2
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• pp.319-327
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• 1999

Zero-Inflated Poisson distributions have been widely used for defect-free products in manufacturing processes. It is very interesting to check the shift after the unknown changepoint. If the detectives are caused by the two different types of factor, we should use bivariate zero-inflated model. In this paper, likelihood ratio tests were used to detect the shift of changes after the changepoint. Some inferences for the parameters in this model were made.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.247-253
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• 1998

In ease of the epidemic Zero-Inflated Poisson model, likelihood ratio test was used for testing epidemic alternatives. Epidemic changepoints were estimated by the method of least squares. It were used for starting points to estimate the maximum likelihood estimators. And several parameters were compared through the Monte Carlo simulations. As a result, maximum likelihood estimators for the epidemic chaagepoints and several parameters are better than the least squares and moment estimators.

• The Korean Journal of Applied Statistics
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• v.24 no.4
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• pp.677-693
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• 2011

In this paper, we consider Bayesian approaches to zero inflated Poisson model, one of the popular models to analyze zero inflated count data. To generate posterior samples, we deal with a Markov Chain Monte Carlo method using a Gibbs sampler and an exact sampling method using an Inverse Bayes Formula(IBF). Posterior sampling algorithms using two methods are compared, and a convergence checking for a Gibbs sampler is discussed, in particular using posterior samples from IBF sampling. Based on these sampling methods, a real data analysis is performed for Trajan data (Marin et al., 1993) and our results are compared with existing Trajan data analysis. We also discuss model selection issues for Trajan data between the Poisson model and zero inflated Poisson model using various criteria. In addition, we complement the previous work by Rodrigues (2003) via further data analysis using a hierarchical Bayesian model.

• The Korean Journal of Applied Statistics
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• v.28 no.3
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• pp.583-592
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• 2015

Zero-inflation has recently attracted much attention in integer-valued time series. This article deals with conditional variance (volatility) modeling for the zero-inflated count time series. We incorporate zero-inflation property into integer-valued GARCH (INGARCH) via conditional Poisson and negative binomial marginals. The Cholera frequency time series is analyzed as a data application. Estimation is carried out using EM-algorithm as suggested by Zhu (2012).

• The Korean Journal of Applied Statistics
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• v.19 no.3
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• pp.505-519
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• 2006

We consider zero-inflated count data, which is discrete count data but has too many zeroes compared to the Poisson distribution. Zero-inflated data can be found in various areas. Despite its increasing importance in practice, appropriate statistical inference on zero-inflated data is limited. Classical inference based on a large number theory does not fit unless the sample size is very large. And regular Poisson model shows lack of St due to many zeroes. To handle the difficulties, a mixture of distributions are considered for the zero-inflated data. Specifically, a mixture of a point mass at zero and a Poisson distribution is employed for the data. In addition, when there exist meaningful covariates selected to the response variable, loglinear link is used between the mean of the response and the covariates in the Poisson distribution part. We propose a Bayesian inference for the zero-inflated Poisson regression model by using a Markov Chain Monte Carlo method. We applied the proposed method to a Korean oral hygienic data and compared the inference results with other models. We found that the proposed method is superior in that it gives small parameter estimation error and more accurate predictions.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.923-932
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• 2014

The Hurdle model can to analyze zero-inflated count data. This model is a mixed model of the logit model for a binary component and a truncated Poisson model of a truncated count component. We propose a new hurdle model with a general heterogeneous random effects covariance matrix to analyze longitudinal zero-inflated count data using modified Cholesky decomposition. This decomposition factors the random effects covariance matrix into generalized autoregressive parameters and innovation variance. The parameters are modeled using (generalized) linear models and estimated with a Bayesian method. We use these methods to carefully analyze a real dataset.

• Journal of the Korean Data and Information Science Society
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• v.14 no.1
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• pp.45-53
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• 2003

The Zero-Inflated Poisson regression is a model for count data with exess zeros. When the reponse variables have excess zeros, it is not easy to apply the Poisson regression model. In this paper, we study and simulate the zero-inflated Poisson regression model. An real example was applied to this model. Regression parameters are estimated by using MLE's. We also compare the fitness of zero-inflated Poisson model with the Poisson regression and decision tree model.