• 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.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.171-190
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• 1993

포아송분포로부터 부의 이항분포로의 이탈을 검색하는 통계량들이 자료의 형태에 따라 여러가지 제시되었다. 그런데 대립가설인 부의 이항분포의 모수화 방법에 따라 분산과 평균의 구조가 변하고 국소 최적 검정 통계량도 달라진다는 것이 알려졌다. 본 논문에서는 대립가설을 일반적인 포아송 혼합분포로까지 확장시키고, 일반적인 형태의 분산과 평균의 구조에도 검정 가능한 새로운 통계량 L을 소개하고 있다. 또한 L 통계량은 포아송 분포로부터 부의 이항분포로의 이탈을 다루는 기존의 여러 통계량들의 일반화된 형태임을 보였다. 점근적 상대효율과 모의 실험을 통하여 L 통계량과 기존의 통계량들을 비교한 결과 분산과 평균사이의 구조에 상관없이 L 통계량이 우수한 것임을 입증하였다.

• 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.153-164
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• 1996

We discussed estimation of parameters using Gibbs sampler under order restriction on the parameters. Two well-knwon probability models, ordered exponential family and binomial distribution, are considered. We derived full conditional distributions(FCD) and also used one-for-one sampling algorithm to sample from the FCD's under order restrictions. Finally through two real data sets we compared three kinds of estimators; isotonic regression estimator, isotonic Bayesian estimator and the estimator using Gibbs sampler.

• 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).

• Journal of the Korean Data and Information Science Society
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• v.27 no.1
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• pp.9-18
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• 2016

In the Heckman-Meyers model, which is frequently referred by IAA, Swiss Solvency Test, EU Solvency II, the assumption of parameter distribution is key factor. While in theory Bayesian analysis somewhat reflects parameter uncertainty using prior distribution, it is often the case where both Heckman-Meyers and Bayesian are necessary to better manage the parameter uncertainty. Therefore, this paper proposes the use of Bayesian H-M CRM, a combination of Heckman-Meyers model and Bayesian, and analyzes its efficiency.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.6
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• pp.2437-2445
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• 2013

The objective of this study is finding the relationship between interstate highway accident frequencies and geometrics using Random Parameter Negative Binomial model. Even though it is impossible to take account of the same design criteria to the all segments or corridors on the road in reality, previous research estimated the fixed value of coefficients without considering each segment's characteristic. The drawback of the traditional negative binomial is not to explain the integrated variations in terms of time and the distinct characters specific segment has. This results in under-estimation of the standard error which inflates the t-value and finally, affects the modeling estimation. Therefore, this study tries to find the relationship of accident frequencies with the heterogeneous geometrics using 9-years and 7-interstate highway data in Washington State area. 16-types of geometrics are used to derive the model which is compared with the traditional negative binomial Model to understand which Model is more suitable. In addition, by calculating marginal effect and elasticity, heterogeneous variables' effect to the accidents are estimated. Hopefully, this study will help to estiblish the future policy of geometrics.

• The Korean Journal of Applied Statistics
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• v.8 no.1
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• pp.159-167
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• 1995

Considering special discrete distribution of exponential family as a sequence with respect to the points of support, the squence is unimodal in some sense. In this paper, we study under what condition the mixture of that discrete distribution with respect to a parameter is unimodal. We derive the maximal interval of the parameter in which each mixture of the discrete distribution such as Binomial and Poisson is always unimodal.

• The Korean Journal of Applied Statistics
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• v.29 no.5
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• pp.823-833
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• 2016

The lifetime is a key characteristic of product quality. It is best to obtain the lifetime data of all samples, but they are often censored due to time or expense limitations. In this paper, we propose a binomial cumulative sum (CUSUM) chart to monitor the mean of type I right-censored Weibull lifetime data, for a xed value of the Weibull shape parameter. We compare the performance of the proposed binomial CUSUM chart with CUSUM charts studied previously using the steady-state average run length (ARL). The results show that the performance of the binomial CUSUM chart is better when the censoring rate is high and/or the sample size is small.