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

• Journal of Korean Society of Transportation
• /
• v.20 no.7
• /
• pp.197-204
• /
• 2002

교통사고예측 및 예방을 위해서는 실제적으로 도로설계과정에서 제어가 가능한 도로 기하구조요소에 대한 사고관계를 파악함이 타당하다. 즉, 도로의 설계자는 도로건설에 앞서 기하구조요소와 사고와의 관계를 현장자료를 통해 정확히 밝혀 도로설계에 반영해야 한다. 이를 위해, 교통사고의 빈도분포를 박히는 것은 가장 기본이 되는 일이며, 교통사고 예측모형개발에 선행되어야 한다. 일반적으로 교통사고건수의 경우 분산이 평균보다 큰 과분산(overdispersion)의 특징을 가지고 있어 음이항 분포를 따른다고 알려져 있다. 따라서 본 논문은 사고모형의 개발에 앞서, 사고발생지점에 대한 도로설계요소와 기타 잠재적인 사고발생 관련요인이 비교적 잘 파악되어있는 호남고속도로를 중심으로 평면 선형상 곡선부에 대하여 교통사고의 분포를 적합도 검정을 통해 알아보고자 하였다. 사고자료는 한국도로송사의 호남고속도로 5년(1996∼2000)간 자료를 분석에 맞게 정리하였으며, 강민욱과 송봉수(2002)에서 제시한 평면선형에 있어서의 구간분할법을 이용하여 배향곡선구간과 단일곡선구간에 대한 사고분석을 하였다. 적합도 분석결과, 예상대로 음이항분포가 사고건수를 설명하기에 가장 적합한 확률분포로 제시되었으며, 이를 통해 최우추정법을 이용한 음이항회귀모형을 개발하였다. 구간분할법을 적용한 음이항회귀모형의 경우, 기존의 확률회귀토형에 비하여 높은 결정계수를 갖았으며, 모형에서 적용된 기하구조요소로는 차량 노출계수, 곡선반경, 단위거리 당 편경사변화값 등이다.

• The Korean Journal of Applied Statistics
• /
• v.28 no.3
• /
• pp.583-592
• /
• 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).

• The Journal of Bigdata
• /
• v.3 no.2
• /
• pp.101-112
• /
• 2018

The purpose of the study is to predict the number of police calls using neural network which is one of the machine learning and negative binomial regression, by using the data of 112 police calls received from Chungnam Provincial Police Agency from June 2016 to May 2017. The variables which may affect the police calls have been selected for developing the prediction model : time, holiday, the day before holiday, season, temperature, precipitation, wind speed, jurisdictional area, population, the number of foreigners, single house rate and other house rate. Some variables show positive correlation, and others negative one. The comparison of the methods can be summarized as follows. Neural network has correlation coefficient of 0.7702 between predicted and actual values with RMSE 2.557. Negative binomial regression on the other hand shows correlation coefficient of 0.7158 with RMSE 2.831. Neural network has low interpretability, but an excellent predictability compared with the negative binomial regression. Based on the prediction model, the police agency can do the optimal manpower allocation for given values in the selected variables.

• Communications of Mathematical Education
• /
• v.21 no.1 s.29
• /
• pp.65-79
• /
• 2007

In this paper we study various aspects of Catalan number with its focus on creative output. As a result we we develop teaching and learning materials for the gifted students which can lead to creative output at the middle school level.

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

• Communications of Mathematical Education
• /
• v.12
• /
• pp.265-280
• /
• 2001

고등학교 수학 I 의 확률 및 통계영역의 교육내용을 정리한 후, 고등학생들에게 확률 및 통계영역에 관한 흥미를 돋구기 위하여 2002년 월드컵을 소재로 한 문제들을 활용하여 비주얼 베이직으로 프로그램한 ‘확률상자’ 라는 확률모형을 개발하였다. 확률상자에는 확률의 역사, 경우의 수, 순열, 같은 것이 있는 순열, 원순열, 조합, 이항계수, 통계적 확률, 조건부 확률, 배반사건 등 모두 10가지 모듈을 포함한다. 확률상자의 초기화면에서 메뉴를 선택하면 선택된 내용에 관한 간단한 정의와 함께 문제가 제시되어 정답을 적도록 하였고, 오답일 때는 힌트를 누르면 정답을 이해할 수 있도록 풀이과정을 제시하였다. 특히, 메뉴가운데서 경우의 수, 순열, 같은 것이 있는 순열, 원순열, 조합, 통계적 확률의 경우에는 풀이과정 중에 애니메이션 또는 시뮬레이션이 실행되도록 하여 이해를 돕도록 하였다.

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

• Journal of Korean Society of Transportation
• /
• v.32 no.6
• /
• pp.662-674
• /
• 2014

In this study, accident frequency prediction models were constructed by collecting variables such as geometric structures, safety facilities, traffic volume and weather conditions, land use, highway design-satisfaction criteria along 780km (4,372 sections) of 4 lane-highways over 8 areas. As for models, a fixed parameter model and a random parameter model were employed. In the random parameter model, some influences were reversed as the range was expressed based on specific probability in the case of no fixed coefficients. In the fixed parameter model, the influences of independent variables on accident frequency were interpreted by using one coefficient, but in the random parameter model, more various interpretations were took place. In particular, curve radius, securement of shoulder lane, vertical grade design criteria satisfaction showed both positive and negative influence, according to specific probability. This means that there could be a reverse effect depending on the behavioral characteristics of drivers and the characteristics of highway sections. Rather, they influence the increase of accident frequency through the all sections.

• Journal of the Korean Data and Information Science Society
• /
• v.26 no.2
• /
• pp.387-397
• /
• 2015

In this paper, the determinants of the number of job changes in the SMEs (small and medium enterprises) youth-intern project is analysed, utilizing SMEs youth-intern DB and employment insurance DB. Since the number of job changes are count data which take integer values other than negative values, general linear regression analysis becomes inappropriate. Therefore, four models such as Poisson regression model, zero inflated Poisson regression model, negative binomial regression model and zero inflated negative binomial regression model are tried to fit count data. A zero inflated negative binomial regression model is selected to be the best model. Major results are the followings. First, the number of job changes is shown to be significantly smaller in the treatment group than in the control group. Second, the number of job changes turns out to be significantly smaller in the young-age group than in the old-age group. Third, it is also shown that the number of job changes of man is significantly greater than that of woman. Lastly, the number of job changes in the bigger firm is shown to be significantly less than that of the smaller firm.