• 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.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.859-869
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• 2000

In this paper, various methods for finding confidence intervals for p of binomial parameter are reviewed. Also we introduce tow bootstrap confidence intervals for p. We compare the performance of bootstrap methods with other methods in terms of average coverage probability by Monte Carlo simulation. Advantages of these bootstrap methods are discussed.

• Journal of the Korean Data and Information Science Society
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• v.21 no.6
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• pp.1109-1115
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• 2010

In this paper, exact confidence interval of hyper-geometric parameter, that is the probability of success p in the population is discussed. Usually, binomial distribution is a well known discrete distribution with abundant usage. Hypergeometric distribution frequently replaces a binomial distribution when it is desirable to make allowance for the finiteness of the population size. For example, an application of the hypergeometric distribution arises in describing a probability model for the number of children attacked by an infectious disease, when a fixed number of them are exposed to it. Exact confidence interval estimation of hypergeometric parameter is reviewed. We consider the performance of exact confidence interval estimates of hypergeometric parameter in terms of actual coverage probability by small sample Monte Carlo simulation.

• The Korean Journal of Applied Statistics
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• v.22 no.1
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• pp.129-140
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• 2009

In this paper, we consider simultaneous confidence intervals for the difference of proportions between two groups taken from multivariate binomial distributions in a nonparametric way. We briefly discuss the construction of simultaneous confidence intervals using the method of adjusting the p-values in multiple tests. The features of bootstrap simultaneous confidence intervals using non-pooled samples are presented. We also compute confidence intervals from the adjusted p-values of multiple tests in the Westfall (1985) style based on a pooled sample. The average coverage probabilities of the bootstrap simultaneous confidence intervals are compared with those of the Bonferroni simultaneous confidence intervals and the Sidak simultaneous confidence intervals. Finally, we give an example that shows how the proposed bootstrap simultaneous confidence intervals can be utilized through data analysis.

• Journal of Information Technology Applications and Management
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• v.28 no.1
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• pp.33-41
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• 2021

In this study, we estimated the number of secondary COVID-19 infections caused by students with potential transmission potential home. When the existing Monte Carlo method was applied to Korean data, the average number of household members of the second COVID-19 infected was predicted. The summary of this study is as follows. First, in general, the number of secondary infections by students returning home from school is greatly influenced by the virus infection rate of each student group they contact while returning home from school. Korea-based empirical research on this is needed. Second, the number of secondary infections by Korean students was relatively lower than that of previous studies. This can be interpreted as being due to the domestic furniture structure. Third, unlike previous studies that assumed the distribution of secondary infected individuals as normal distribution, assuming a negative binomial distribution, the number of secondary infected individuals was sensitively changed according to the estimated parameters. Interpretation of this result shows that the number of secondary infections may vary depending on the time of decision making, the target region, and the target student group. Finally, according to the results of this analysis, a proposal was made to support education policy decisions.

• The Korean Journal of Applied Statistics
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• v.27 no.3
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• pp.445-459
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• 2014

As a certain job is repeatedly done by a worker, the outcome comparative to the effort to complete the job gets more remarkable. The outcome may be the time required and fraction defective. This phenomenon is referred to a learning-curve effect. We focus on the parametric modeling of the learning-curve effects on count data using a logistic cumulative distribution function and some probability mass functions such as a Poisson and negative binomial. We conduct various simulation scenarios to clarify the characteristics of the proposed model. We also consider a real application to compare the two discrete-type distribution functions.

• The Korean Journal of Applied Statistics
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• v.18 no.3
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• pp.607-615
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• 2005

Recently the interval estimation of a binomial proportion is revisited in various literatures. This is mainly due to the erratic behavior of the coverage probability of the will-known Wald confidence interval. Various alternatives have been proposed. Among them, Agresti-Coull confidence interval has been recommended by Brown et al. (2001) with other confidence intervals for large sample, say n $\ge$ 40. On the other hand, a noninformative Bayesian approach called Polya posterior often produces statistics with good frequentist's properties. In this note, an interval estimator is developed using weighted Polya posterior. The resulting interval estimator is essentially the Agresti-Coull confidence interval with some improved features. It is shown that the weighted Polys posterior produce an effective interval estimator for small sample size and a severely skewed binomial distribution.

• Communications for Statistical Applications and Methods
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• v.18 no.5
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• pp.571-579
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• 2011

We propose a new bivariate zero-inflated negative binomial regression model to allow heterogeneous dispersions. To show the performance of our proposed model, Health Care data in Deb and Trivedi (1997) are used to compare it with the other bivariate zero-inflated negative binomial model proposed by Wang (2003) that has a common dispersion between the two response variables. This empirical study shows better results from the views of log-likelihood and AIC.

• 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.

• Communications for Statistical Applications and Methods
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• v.16 no.3
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• pp.501-509
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• 2009

Recently the interval estimation of binomial proportions is revisited in various literatures. This is mainly due to the erratic behavior of the coverage probability of the well-known Wald confidence interval. Various alternatives have been proposed. Among them, the Agresti-Coull confidence interval, the Wilson confidence interval and the Bayes confidence interval resulting from the noninformative Jefferys prior were recommended by Brown et al. (2001). However, unlike the binomial distribution case, little is known about the properties of the confidence intervals in finite population sampling. In this note, the property of confidence intervals is investigated in anile population sampling.