• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.585-594
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• 2003

It has been generally recognized that conventional binomial or Poisson model provides poor fits to the actual correlated binary data due to the extra-binomial variation. A number of generalized statistical models have been proposed to account for this additional variation. Among them, beta-binomial, correlated-binomial, and modified-binomial models are binomial-related models which are frequently used in modeling the sum of n correlated binary data. In many situations, it is reasonable to assume that n correlated binary data are exchangeable, which is a special case of correlated binary data. The sum of n exchangeable correlated binary data is modeled relatively well when the above three binomial-related models are applied. But the estimation results of correlation coefficient turn to be quite different. Hence, it is important to identify which model provides better estimates of model parameters(success probability, correlation coefficient). For this purpose, a small-scale simulation study is performed to compare the behavior of above three models.

• Journal of Korean Society for Quality Management
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• v.45 no.2
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• pp.209-225
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• 2017

Purpose: Since traditional p chart is unable to deal with the variation of attribute data, this paper proposes a new attribute control chart for nonconforming proportions incorporating overdispersion with a beta-binomial model. Methods: Statistical theories for control chart developed under the beta-binomial model and a new approach using this control chart are presented Results: False alarm probabilities of p chart with the beta-binomial model are evaluated and demerits of p chart under overdispersion are discussed from three examples. Hence a concrete procedure for the proposed control chart is provided and illustrated with examples Conclusion: The proposed chart is more useful than traditional p chart, individual chart to treat observed proportions nonconforming as variable data and Laney p' chart.

• The Korean Journal of Applied Statistics
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• v.22 no.2
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• pp.271-280
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• 2009

For bivariate binomial data with both intra and inter-class correlation, Danaher and Hardie (2005) proposed a bivariate beta-binomial model. However, the model is limited to the situation where the intra-class correlation is strictly positive. Thus it might be seriously inadequate for data with a negative intra-class correlation. Several authors have considered generalized binomial distributions covering a wider range of intra-class correlation which could relax the possible model restrictions imposed. Among others there are the additive/multiplicative and the beta/extended beta binomial model. In this study, bivariate models of the Sarmanov (1966) type are formed by combining each of those univariate models to take care of the inter-class correlation, and are evaluated in terms of the goodness-of-fit. As a result, B-mB and B-ebB are fitted, successfully, to real data and that B-mB, which has a wider permissible range than B-ebB for the intra-class correlation is relatively preferred.

• 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.

• Horticultural Science & Technology
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• v.30 no.5
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• pp.596-602
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• 2012

Infestations of Aphis gossypii per leaf in greenhouse cultivation of cucumbers were investigated to develop binomial sampling plans. An empirical $P_T-m$ model, $ln(m)={\alpha}+{\beta}ln[-ln(1-P_T)]$, was used to evaluate relationship between the proportion of infested leaves with ${\leq}$ T aphids per leaf ($P_T$) and mean aphid density (m). Tally thresholds (T) were set to 1, 3, 5, 7, and 9 aphids per leaf to find appropriate T in greenhouse cultivation of cucumbers. Increasing sample size had little effect on the precision of the binomial sampling plan. However, the precision increased with tally threshold. The binomial model with T = 5 provided appropriate predictions of the mean densities of A. gossypii in the greenhouse cultivation of cucumbers. Using a binomial model with T = 5 (sample size = 200), a wide range of densities (1.2 - 222.8 aphids per leaf) could be estimated with precision levels of 0.346 - 0.380 for $P_T$ values between 0.15 and 0.96. Binomial models were validated at T = 5 and 7 using 12 independent data sets. Both binomial models were robust and adequately described aphid densities; most of the independent sampling data fell within 95% confidence intervals around the prediction model.

• Journal of the Korean Statistical Society
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• v.31 no.1
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• pp.45-61
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• 2002

We consider the problem of estimating binomial proportions in the presence of nonignorable nonresponse using the Bayesian selection approach. Inference is sampling based and Markov chain Monte Carlo (MCMC) methods are used to perform the computations. We apply our method to study doctor visits data from the Korean National Family Income and Expenditure Survey (NFIES). The ignorable and nonignorable models are compared to Stasny's method (1991) by measuring the variability from the Metropolis-Hastings (MH) sampler. The results show that both models work very well.

• 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.

• The Korean Journal of Applied Statistics
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• v.7 no.2
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• pp.9-19
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• 1994

Beta-binomial model, which is reparametrized in terms of the mean probability $\mu$ of a positive deagnosis and the $\kappa$ of agreement, is widely used in psychology. When $\mu$ is close to 0, inference about $\kappa$ become difficult because likelihood function becomes constant. We consider Bayesian approach in this case. To apply Bayesian analysis, Gibbs sampler is used to overcome difficulties in integration. Marginal posterior density functions are estimated and Bayesian estimates are derived by using Gibbs sampler and compare the results with the one obtained by using numerical integration.

• Korean journal of applied entomology
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• v.40 no.3
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• pp.197-202
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• 2001

The density of citrus red mite(CRM), Panonychus citri(McGregor), on the commercial satsuma mandarin Citrus unshiu L. groves were determined by counts of the number of CRM per leaf using by leaf sample in Jeju for 2 years. Binomial sampling plans were developed based on the relationship between the mean density per leaf(m) and the proportion of leaf infested with less than T mites per leaf($P_{T}$), according to the empirical model $ln(m)={\alpha}+{\beta}ln(-ln(1-P_{T}))$. T was defined as tally threshold, and set to 1, 3, 5 and 7 mites per leaf in this study. Increasing sample size, regardless of tally threshold, had little effects on the precision of the binomial sampling plan. Increasing sampling size had little effect on the precision of the estimated mean regardless of tally thresholds. T=1 was chosen as the best tally threshold for estimating densities of CRM based on the precision of the model. The binomial model with T=1 provided reliable predictions of mean densities of CRM observed on the commercial satsuma mandarin groves. Binomial sequential sampling procedure were developed for classifying the density of CRM. A binomial sampling program for decision-making CRM population level based on action threshold of 2 mites per leaf was obtained.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.507-516
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• 2011

Comparative studies on generalized binomial models (Moon, 2003; Ng, 1989; Paul, 1985; Kupper and Haseman, 1978; Griffiths, 1973) are restrictive in that the models compared are rather limited and MSE of the estimates is the only measure considered for the model adequacy. This paper is aimed to report simulation results which provide possible guidelines for selecting a proper model. We examine Pearson type of goodness-of-fit statistic to its degrees of freedom and AIC for the overall model quality. MSE and Bias of the individual estimates are also considered as the component fit measures. Performance of some models varies widely for a certain range of the parameter space while most of the models are quite competent. Our evaluation shows that the Extended Beta-Binomial model (Prentice, 1986) turns out to be particularly favorable in the point that it provides consistently excellent fit almost all over the values of the intra-class correlation coefficient and the probability of success.