• Journal of Korean Society of Industrial and Systems Engineering
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• v.28 no.2
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• pp.146-151
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• 2005

Some distributions have been used for diagnosing the lead time demand distribution in inventory system. In this paper, we describe the negative binomial distribution as a suitable demand distribution for a specific retail inventory management application. We here assume that customer order sizes are described by the Poisson distribution with the random parameter following a gamma distribution. This implies in turn that the negative binomial distribution is obtained by mixing the mean of the Poisson distribution with a gamma distribution. The purpose of this paper is to give an interpretation of the negative binomial demand process by considering the sources of variability in the unknown Poisson parameter. Such variability comes from the unknown demand rate and the unknown lead time interval.

• 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.

• Communications for Statistical Applications and Methods
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• v.18 no.5
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• pp.615-623
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• 2011

Several methods are used in interval estimation for binomial proportion; however the coverage probabilities of most confidence intervals depart from the confidence level when the binomial population proportion closes to 0 or 1 due to the extreme value. Vollset (1993), Agresti and Coull (1998), Newcombe (1998), and Brown et al. (2001) suggested methods to adjust the extreme value. This paper discusses the influence of extreme value in a binomial confidence interval through the numerical comparison of 6 confidence intervals.

• Communications for Statistical Applications and Methods
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• v.16 no.5
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• pp.731-743
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• 2009

The interval estimation for binomial proportion has been treated practically as well as theoretically for a long time. In this paper we compared the properties of major confidence intervals and summarized current issues for coverage probability and interval length which are the criteria of evaluation for confidence interval. Additionally, we examined the three topics which were considered in using the binomial confidence interval in the field. And finally we discussed the future studies for a low binomial proportion.

• Communications for Statistical Applications and Methods
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• v.19 no.6
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• pp.809-817
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• 2012

We propose a semiparametric inference for a generalized varying coefficient partially linear model(VCPLM) for negative binomial data. The VCPLM is useful to model real data in that varying coefficients are a special type of interaction between explanatory variables and partially linear models fit both parametric and nonparametric terms. The negative binomial distribution often arise in modelling count data which usually are overdispersed. The varying coefficient function estimators and regression parameters in generalized VCPLM are obtained by formulating a penalized likelihood through smoothing splines for negative binomial data when the shape parameter is known. The performance of the proposed method is then evaluated by simulations.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.28 no.4
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• pp.79-84
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• 2005

Some distributions have been used for diagnosing the lead time demand distribution in inventory system. In this paper, we describe the negative binomial distribution as a suitable demand distribution for a specific retail inventory management application. We here assume that customer order sizes are described by the Poisson distribution with the random parameter following a gamma distribution. This implies in turn that the negative binomial distribution is obtained by mixing the mean of the Poisson distribution with a gamma distribution. The purpose of this paper is to give an interpretation of the negative binomial demand process by considering the sources of variability in the unknown Poisson parameter. Such variability comes from the unknown demand rate and the unknown lead time interval.

• Communications of Mathematical Education
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• v.23 no.4
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• pp.1079-1092
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• 2009

The purpose of this study is to investigate Newton's binomial theorem that was on epistemological basis of the emergent background and developmental course of infinite series and power series. Through this investigation, it will be examined how finding the approximate of square root of given numbers, the method of the inverse method of fluxions by Newton, and Gregory and Mercator series were developed in the course of history of mathematics. As the result of this study pedagogical analysis and discussion of the history of mathematics on Newton's binomial theorem will be presented.

• Journal of the Korean Regional Science Association
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• v.31 no.3
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• pp.39-54
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• 2015

To assess an economic value of Cheonggyecheon river restoration project, an in-depth exit survey data was collected to apply travel cost method in this study. Poisson model, Negative Binomial, Zero-truncated Poisson, and Zero-truncated Negative Binomial model were executed due to the nature of count data. Empirical results showed that regressors were statistically significant and corresponded to general consumer theory. Since our survey data showed over-dispersion, Zero-truncated Negative Binomial was selected as an optimal one to analyze travel demand of Cheonggyecheon by model goodness of fit test among those aforementioned empirical models. Estimating an economic value of Cheonggyecheon river restoration project, which is known as an ecological river restoration project, we used annual visit of individual traveler and an optimal model. Suffice to say that the annual economic value of Cheonggyecheon river restoration project was estimated as 193.4 billion won in 2013.

• Journal of the Korean School Mathematics Society
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• v.19 no.3
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• pp.291-308
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• 2016

In this paper, we did a study on the definition and properties of binomial coefficients which can be seen with the topic for the enrichment of mathematically gifted students. Using this result, studied the problem of how to solve equations containing the binomial coefficients by using the mathematical induction, binomial theorem, the definition of the combination, and road network model situations. And such contents can be adequately dealt with the subject of mathematics enrichment gifted and talented Education because mathematically gifted students may well be the subject of inquiry. In addition, it can be used to study the subject to experience a deep sense of mathematics. As this research, it will be introduced as an example to guide students.

• 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.