• Journal of the Korean Statistical Society
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• v.36 no.2
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• pp.321-333
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• 2007

In the proportional hazard model with the beta process prior, the posterior computation with the discrete approximation is considered. The time period of interest is partitioned by small intervals. On each partitioning interval, the likelihood is approximated by that of a binomial experiment and the beta process prior is by a beta distribution. Consequently, the posterior is approximated by that of many independent binomial model with beta priors. The analysis of the leukemia remission data is given as an example. It is illustrated that the length of the partitioning interval affects the posterior and one needs to be careful in choosing it.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.1
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• pp.55-72
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• 2009

A misclassified size-biased modified power series distribution (MSBMPSD) where some of the observations corresponding to x = c + 1 are misclassified as x = c with probability $\alpha$, is defined. We obtain its recurrence relations among the raw moments, the central moments and the factorial moments. Discussion of the effect of the misclassification on the variance is considered. To illustrate the situation under consideration some of its particular cases like the size-biased generalized negative binomial (SBGNB), the size-biased generalized Poisson (SBGP) and sizebiased Borel distributions are included. Finally, an example is presented for the size-biased generalized Poisson distribution to illustrate the results.

• The Korean Journal of Applied Statistics
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• v.25 no.6
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• pp.1037-1047
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• 2012

The generalized linear mixed model(GLMM) is widely used in fitting categorical responses of clustered data. In the numerical approximation of likelihood function the normality is assumed for the random effects distribution; subsequently, the commercial statistical packages also routinely fit GLMM under this normality assumption. We may also encounter departures from the distributional assumption on the response variable. It would be interesting to investigate the impact on the estimates of parameters under misspecification of distributions; however, there has been limited researche on these topics. We study the sensitivity or robustness of the maximum likelihood estimators(MLEs) of GLMM for counts data when the true underlying distribution is normal, gamma, exponential, and a mixture of two normal distributions. We also consider the effects on the MLEs when we fit Poisson-normal GLMM whereas the outcomes are generated from the negative binomial distribution with overdispersion. Through a small scale Monte Carlo study we check the empirical coverage probabilities of parameters and biases of MLEs of GLMM.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.61-70
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• 2018

Modeling of the random effects covariance matrix in generalized linear mixed models (GLMMs) is an issue in analysis of longitudinal categorical data because the covariance matrix can be high-dimensional and its estimate must satisfy positive-definiteness. To satisfy these constraints, we consider the autoregressive and moving average Cholesky decomposition (ARMACD) to model the covariance matrix. The ARMACD creates a more flexible decomposition of the covariance matrix that provides generalized autoregressive parameters, generalized moving average parameters, and innovation variances. In this paper, we analyze longitudinal count data with overdispersion using GLMMs. We propose negative binomial loglinear mixed models to analyze longitudinal count data and we also present modeling of the random effects covariance matrix using the ARMACD. Epilepsy data are analyzed using our proposed model.

• Journal of Korean Society for Quality Management
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• v.10 no.2
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• pp.25-33
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• 1982

We discuss a model for acceptance/rejection decision regarding finite populations. The model is based on a beta-binomial prior distribution and additive costs -- relative sampling costs, relative sorting costs and costs of accepted defectives. A substantial part of the paper is devoted to constructing a Bayes sequential sampling acceptance plan (BSSAP) for attributes under the model. It is shown that the Bayes fixed size sampling acceptance plans (BFSAP) are better than the Hald's (1960) single sampling acceptance plans based on a uniform prior. Some tables and examples are provided for comprisons of the minimum Bayes risks of the BSSAP and those of the BFSAP based on a uniform prior and the model.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.385-391
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• 2003

A sequence of n Bernoulli trials which violates the constant success probability assumption is termed as "Poisson trials". In this paper, the recurrence formula for the r-th central moment of number of successes with n Poisson trials is derived. Romanovsky's method, based on the differentiation of characteristic function, is used in the derivation of recurrence formula for the central moments of conventional binomial distribution. Romanovsky's method is applied to that of Poisson trials in this paper. Some central moment calculation results are given to compare the central moments of Poisson trials with those of conventional binomial distribution.

• Journal of the Korean Society of Safety
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• v.29 no.6
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• pp.151-157
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• 2014

This study deals with the rear-end collision at roundabouts. The purpose of this study is to develop the accident models of rear-end collision in Korea. In pursuing the above, this study gives particular attention to developing the appropriate models using Poisson, negative binomial model, ZAM, multiple linear and nonlinear regression models, and statistical analysis tools. The main results are as follows. First, the Vuong statistics and overdispersion parameters indicate that ZIP is the most appropriate model among count data models. Second, RMSE, MPB, MAD and correlation coefficient tests show that the multiple nonlinear model is the most suitable to the rear-end collision data. Finally, such the independent variables as traffic volume, ratio of heavy vehicle, number of circulatory roadway lane, number of crosswalk and stop line are adopted in the optimal model.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.199-205
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• 1999

This paper discusses the generalized mixed-effects model for the analysis of overdispersed binomial data. Sometimes certain types of sampling designs or genetic characters of experimental units can be regarded as factors of extra binomial variation. For such cases, this paper suggests models with one or two random effects to explain overdispersion caused by those affecting factors and shows how to test for a model adequacy based on deviance.

• Communications for Statistical Applications and Methods
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• v.3 no.2
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• pp.175-185
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• 1996

For the Change-point problem in a sequence of binomial variables we consider the maximum likelihood estimator (MLE) of unknown change-point. Its asymptotic distribution is quite limited in the case of binomial variables with different numver of trials at each time point. Hinkley and Hinkley (1970) gives an asymptotic distribution of the MLE for a sequence of Bernoulli random variables. To find the asymptotic distribution a numerical method such as bootstrap can be used. Another concern of our interest in the inference on the change-point and we derive confidence sets based on the liklihood ratio test(LRT). We find approximate confidence sets from the bootstrap distribution and compare the two results through an example.

• International journal of advanced smart convergence
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• v.10 no.4
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• pp.215-224
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• 2021

The purpose of this study is to estimate the factors that affect college students' drinking needs and spending. An analysis model to estimate the determinants affecting drinking needs was applied with a truncated Poisson model and a truncated negative binomial model. Tests to select more appropriate models of the two types were made using the comparison of log-likelihood function and the over-dispersion test. The analysis result was interpreted by applying the truncated negative binomial model as the truncated Poisson model showed over-dispersion. We also applied the Tobit model to analyze the determinantsthat affect college students' expenditure on drinking. According to the analysis, gender, grade, allowance and parental occupation were the factors influencing statistics, and gender, type of household income, and student religion were the factors influencing expenditure.