• Journal of Korean Society of Transportation
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• v.20 no.7
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• pp.197-204
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• 2002

교통사고예측 및 예방을 위해서는 실제적으로 도로설계과정에서 제어가 가능한 도로 기하구조요소에 대한 사고관계를 파악함이 타당하다. 즉, 도로의 설계자는 도로건설에 앞서 기하구조요소와 사고와의 관계를 현장자료를 통해 정확히 밝혀 도로설계에 반영해야 한다. 이를 위해, 교통사고의 빈도분포를 박히는 것은 가장 기본이 되는 일이며, 교통사고 예측모형개발에 선행되어야 한다. 일반적으로 교통사고건수의 경우 분산이 평균보다 큰 과분산(overdispersion)의 특징을 가지고 있어 음이항 분포를 따른다고 알려져 있다. 따라서 본 논문은 사고모형의 개발에 앞서, 사고발생지점에 대한 도로설계요소와 기타 잠재적인 사고발생 관련요인이 비교적 잘 파악되어있는 호남고속도로를 중심으로 평면 선형상 곡선부에 대하여 교통사고의 분포를 적합도 검정을 통해 알아보고자 하였다. 사고자료는 한국도로송사의 호남고속도로 5년(1996∼2000)간 자료를 분석에 맞게 정리하였으며, 강민욱과 송봉수(2002)에서 제시한 평면선형에 있어서의 구간분할법을 이용하여 배향곡선구간과 단일곡선구간에 대한 사고분석을 하였다. 적합도 분석결과, 예상대로 음이항분포가 사고건수를 설명하기에 가장 적합한 확률분포로 제시되었으며, 이를 통해 최우추정법을 이용한 음이항회귀모형을 개발하였다. 구간분할법을 적용한 음이항회귀모형의 경우, 기존의 확률회귀토형에 비하여 높은 결정계수를 갖았으며, 모형에서 적용된 기하구조요소로는 차량 노출계수, 곡선반경, 단위거리 당 편경사변화값 등이다.

• Journal of the Korean Data and Information Science Society
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• v.28 no.1
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• pp.153-161
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• 2017

Branching processes which is used for epidemic dispersion as stochastic process model have advantages to estimate parameters by real data. We have to estimate both mean and dispersion parameter in order to use the negative binomial distribution as an offspring distribution on branching processes. In existing studies on biology and epidemiology, it is estimated using maximum-likelihood methods. However, for most of epidemic data, it is hard to get the best precision of maximum-likelihood estimator. We suggest a Bayesian inference that have good properties of statistics for small-sample. After estimating dispersion parameter we modelled the posterior distribution for 2015 Korea MERS cases. As the result, we found that the estimated dispersion parameter is relatively stable no matter how we assume prior distribution. We also computed extinction probabilities on branching processes using estimated dispersion parameters.

• 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.21 no.2
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• pp.341-353
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• 2008

The bootstrap method for the score test statistic is proposed in a bivariate negative binomial distribution. The Monte Carlo study shows that the score test for testing overdispersion underestimates the nominal significance level, while the score test for "intrinsic correlation" overestimates the nominal one. To overcome this problem, we propose a bootstrap method for the score test. We find that bootstrap methods keep the significance level close to the nominal significance level for testing the hypothesis. An empirical example is provided to illustrate the results.

• The Korean Journal of Applied Statistics
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• v.35 no.2
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• pp.311-325
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• 2022

For count responses, the situation of excess zeros often occurs in various research fields. Zero-inflated model is a common choice for modeling such count data. Bayesian inference for the zero-inflated model has long been recognized as a hard problem because the form of conditional posterior distribution is not in closed form. Recently, however, Pillow and Scott (2012) and Polson et al. (2013) proposed a Pólya-Gamma data-augmentation strategy for logistic and negative binomial models, facilitating Bayesian inference for the zero-inflated model. We apply Bayesian zero-inflated negative binomial regression model to longitudinal pharmaceutical data which have been previously analyzed by Min and Agresti (2005). To facilitate posterior sampling for longitudinal zero-inflated model, we use the Pólya-Gamma data-augmentation strategy.

• The Korean Journal of Applied Statistics
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• v.31 no.6
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• pp.733-749
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• 2018

Sample selection arises as a result of the partial observability of the outcome of interest in a study. Heckman introduced a sample selection model to analyze such data and proposed a full maximum likelihood estimation method under the assumption of normality. Recently sample selection models for binomial and Poisson response variables have been proposed. Based on the theory of symmetry-modulated distribution, we extend these to a model for overdispersed count data. This type of data with no sample selection is often modeled using negative binomial distribution. Hence we propose a sample selection model for overdispersed count data using the negative binomial distribution. A real data application is employed. Simulation studies reveal that our estimation method based on profile log-likelihood is stable.

• The Korean Journal of Applied Statistics
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• v.9 no.1
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• pp.111-124
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• 1996

In this paper, we consider the first-order integer valued autoregressive(INAR(1)) model where correlation structure is similar to that of the continuous valued AR(1) process. Several methods for estimating the parameters of the INAR(1) process with negative binomial marginal are discussed. We derive asymptotic distributions of these estimators. The results of a simulation study for these estimators methods show that the estimator which we present in this paper is better than the estimator which Klimko and Nelson(1978) presented. As an application we considered the estimator of M/M/1 queue length.

• The Korean Journal of Applied Statistics
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• v.23 no.3
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• pp.585-594
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• 2010

This study, investigates the effects of dispersion parameters between two response variables in zero-truncated bivariate generalized Poisson distributions. A Monte Carlo study shows that the zero-truncated bivariate Poisson and negative binomial models fit poorly wherein the zero-truncated bivariate count data has heterogeneous dispersion parameters on dependent variables. In addition, we derive the score test for testing the equality of the dispersion parameters and compare its efficiency with the likelihood ratio test.

• Communications for Statistical Applications and Methods
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• v.18 no.2
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• pp.219-227
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• 2011

In this paper, we proposed a generalized bivariate negative binomial distribution allowing heterogeneous dispersions on two dependent variables based on a trivariate reduction technique. In this model, we propose the score and LR tests for testing the equality of dispersions and compare the efficiencies of the proposed tests using a Monte Carlo study. The Monte Carlo study shows that the proposed score and LR tests prove to be an efficient test for the equality of dispersions in the view of the significance level and power. However, the score test is easier to compute than the LR test and it shows a slightly better performance than the LR test from the Monte Carlo study, we suggest the use of score tests for testing the equality of dispersions on two dependent variables. In addition, an empirical example is provided to illustrate the results.

• The Korean Journal of Applied Statistics
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• v.6 no.1
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• pp.41-52
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• 1993

In this paper we study numerical behavior of the adjustments for the variances of the pearson and deviance type dispersion statistics in two overdispersed mixture models; negative binomial and beta-binomial distribution. They are important families of an extended quasi-likelihood model which is very useful for the joint modelling of mean and dispersion. Comparisons are done for two types of dispersion statistics for various mean and dispersion parameters by simulation studies.