• 산업경영시스템학회지
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• 제28권2호
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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.

• 산업경영시스템학회지
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• 제28권4호
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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.

• International Journal of Contents
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• 제2권2호
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• pp.17-24
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• 2006

The work presented in this paper is divided into two parts. The first part presents finite urn problems which generate truncated negative binomial random variables. Some combinatorial identities that arose from the negative binomial sampling and truncated negative binomial sampling are established. These identities are constructed and serve important roles when we deal with these distributions and their characteristics. Other important results including cumulants and moments of the distributions are given in somewhat simple forms. Second, the distributions of the maximum of two chi-square variables and the distributions of the maximum correlated F-variables are then derived within the negative binomial sampling scheme. Although multinomial theory applied to order statistics and standard transformation techniques can be used to derive these distributions, the negative binomial sampling approach provides more information and deeper insight regarding the nature of the relationship between the sampling vehicle and the probability distributions of these functions of chi-square variables. We also provide an algorithm to compute the percentage points of these distributions. We supplement our findings with exact simple computational methods where no interpolations are involved.

• International Journal of Contents
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• 제3권1호
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• pp.1-8
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• 2007

The distributions of the minimum correlated F-variable arises in many applied statistical problems including simultaneous analysis of variance (SANOVA), equality of variance, selection and ranking populations, and reliability analysis. In this paper, negative binomial sampling technique is employed to derive the distributions of the minimum of chi-square variables and hence the distributions of the minimum correlated F-variables. The work presented in this paper is divided in two parts. The first part is devoted to develop some combinatorial identities arised from the negative binomial sampling. These identities are constructed and justified to serve important purpose, when we deal with these distributions or their characteristics. Other important results including cumulants and moments of these distributions are also given in somewhat simple forms. Second, the distributions of minimum, chisquare variable and hence the distribution of the minimum correlated F-variables are then derived within the negative binomial sampling framework. Although, multinomial theory applied to order statistics and standard transformation techniques can be used to derive these distributions, the negative binomial sampling approach provides more information regarding the nature of the relationship between the sampling vehicle and the probability distributions of these functions of chi-square variables. We also provide an algorithm to compute the percentage points of the distributions. The computation methods we adopted are exact and no interpolations are involved.

• Communications for Statistical Applications and Methods
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• 제14권1호
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• pp.23-32
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• 2007

We consider penalized likelihood regression with data from the negative binomial distribution with unknown shape parameter. Smoothing parameter selection and asymptotically efficient low dimensional approximations are employed for negative binomial data along with shape parameter estimation through several different algorithms.

• Journal of the Korean Statistical Society
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• 제11권2호
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• pp.131-138
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• 1982

Analogous to Singh's (1978) characterization of positive-Poisson distributioin and Shanmugam and Singh's (1992) characterization of logarithmic series distribution, a characterization and its statistical application of the negative binomial distribution truncated at zero are given in this paper. While it is known that under certain conditions the negative binomial distribution truncted at zero approaches the positive-Poisson and the logarithmic series distributions, we show here that the results of this paper approach in limit the results of Singh, and Shanmugam and Singh, respectively. Using the biologicla data from Sampford (1955), we illusrate our results. Also, expressions are explicitly given to test the hypothesis whether a random sample is indeed from a geometric distribution.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권2호
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• pp.15-29
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• 2007

In this paper, we explore some interesting models of the quasi-negative-binomial distribution based on difference differential equations applicable to theory of microorganisms and the situations like that. Some characterizations based on conditional distributions and damage process have been obtained. Further, the distribution of number of accidents as the quasi-negative-binomial distribution in the light of Irwin's theory of ";proneness-liability"; model has been derived. Finally, the proposed model (QNBD) has been applied to study the Shunting accidents, home injuries, and strikes in industries.

• 대한교통학회지
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• 제25권3호
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• pp.123-135
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• 2007

본 연구에서는 고속도로 트럼펫 인터체인지상에서 연결로 형식별로 일어나는 교통사고와 도로 기하구조 및 교통량등의 교통사고 요인들과의 관계를 분석하기 위해 교통사고의 분포의 특성을 분석하여 적합도 검증을 통해 모형추정시 가장 적절한 분포를 찾은 결과 음이항분포(Negative binomial distribution)가 선택되었다. 선택된 분포에 기반하여 트럼펫 인터체인지 연결로 전체, 연결로 형식별(직결, 준직결, 루프연결로) 각각의 음이항회귀모형 (Negative binomial regression model)을 개발하였다. 총 4개의 모형을 개발하고 그것의 적합도를 판단하는 여러 가지 통계값과 모형에서 예측한 값과 실제 관측값과의 차이를 분석한 결과 예측모형이 적합하게 구축되었음을 보였다. 추정된 모형의 통계적으로 유의한 변수들을 분석하여 교통사고를 설명하는데 유의한 변수들을 판단하고 이러한 변수들을 도로의 설계자가 도로 설계 및 운영에 적용하거나 교통안전계획 수립시 해당도로의 교통특성을 반영한 교통사고 절감 대책 등에 이용할 수 있을 것이다.

• Communications for Statistical Applications and Methods
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• 제19권6호
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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 the Korean Data and Information Science Society
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• 제22권4호
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• pp.811-817
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• 2011

We shall introduce a general probability mass function which includes several discrete probability mass functions. Especially, when the random variable X is Poisson, binomial, and negative binomial random variables as some special cases of the introduced distribution, the maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE) of the probability P(X ${\leq}$ t) are considered. And the efficiencies of the MLE and the UMVUE of the reliability ar compared each other.