• 제목/요약/키워드: Multinomial coefficients

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Multinomial Probability Distribution and Quantum Deformed Algebras

  • Fridolin Melong
    • Kyungpook Mathematical Journal
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    • 제63권3호
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    • pp.463-484
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    • 2023
  • An examination is conducted on the multinomial coefficients derived from generalized quantum deformed algebras, and on their recurrence relations. The 𝓡(p, q)-deformed multinomial probability distribution and the negative 𝓡(p, q)-deformed multinomial probability distribution are constructed, and the recurrence relations are determined. From our general result, we deduce particular cases that correspond to quantum algebras considered in the literature.

개인별 선택행위에서의 동력모형의 유효성 (Validity of Gravity Models for Individual Choies)

  • 음성직
    • 대한교통학회지
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    • 제1권1호
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    • pp.43-47
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    • 1983
  • Within the conventional transportation planning process, "trip distribution" has a significant role to play. The most widely applied trip distribution model is the gravity model, for which Wilson provided the theoretical basis in 1967. The concept of the gravity model, however, still remains ambiguous if we analyze the "trip distribution" with a disaggregate data set. Thus, this paper hypothesizes that the gravity technique is still valid even with the disaggregate data set, by proving that the estimated coefficients of the gravity model, which is derived under the principle of entropy maximization, are identical with those of the multinomial logit model, which is derived under the principle of individual utility maximization.tility maximization.

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Collapsibility and Suppression for Cumulative Logistic Model

  • Hong, Chong-Sun;Kim, Kil-Tae
    • Communications for Statistical Applications and Methods
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    • 제12권2호
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    • pp.313-322
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    • 2005
  • In this paper, we discuss suppression for logistic regression model. Suppression for linear regression model was defined as the relationship among sums of squared for regression as well as correlation coefficients of. variables. Since it is not common to obtain simple correlation coefficient for binary response variable of logistic model, we consider cumulative logistic models with multinomial and ordinal response variables rather than usual logistic model. As number of category of a response variable for the cumulative logistic model gets collapsed into binary, it is found that suppressions for these logistic models are changed. These suppression results for cumulative logistic models are discussed and compared with those of linear model.

4대강 하구의 속성 가치 추정 -다항로짓모형에서 IIA가정의 검토와 대안 모형을 중심으로- (Estimating the Attribute Values of 4 Major River Estuaries in Korea -Focusing on Testing for the IIA Assumption in MNL Model and the Alternative Models-)

  • 신영철
    • 자원ㆍ환경경제연구
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    • 제22권3호
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    • pp.521-545
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    • 2013
  • 본 연구는 우리나라 4대강(한강, 금강, 영산강, 낙동강) 하구의 중요 속성(하구 유형, 하구 하천 수질, 하구 해수역 수질, 하구 생물다양성 수준)과 관련된 가치를 도출하기 위하여 진술선호법에 속하는 선택실험법(CE)을 이용하였다. 선택실험법에서 얻어진 자료에 대해서는 일반적으로 다항로짓모형(MNL)으로 분석하지만, 다항로짓모형의 기본 가정에 해당하는 IIA 성립 여부를 Hausman과 McFadden(1984)이 제시한 검정 통계량으로 검토한 결과에 따르면 본 연구 자료에서 IIA 가정은 모두 기각되었다. 그러므로 IIA의 가정을 완화한 이분산극치모형(HEV)과 다항프로빗모형(MNP)으로 분석한 결과, IIA 가정을 충족하지 못하는 자료를 다항로짓모형으로 분석하면 그로부터 도출된 추정계수 및 속성의 경제적 가치들을 상당히 왜곡하는 것으로 파악되었다. 다항프로빗모형(MNP)의 추정 결과에 따르면, 4대강에 속하는 한 하구가 자연 하구인 경우의 경제적 가치는 3,523억원(95% 신뢰구간 2,611억원~4,778억원)이다. 4대강에 속하는 한 하구 하천 수질이 한 등급 상승하면 4,115억원(95% 신뢰구간 3,385억원~5,255억원)의 경제적 가치를 갖는다. 한편 4대강 하구에 속하는 한 하구의 해수역 수질이 한 등급 상승하면 3,589억원(95% 신뢰구간 2,925억원~4,570억원)의 경제적 가치가 증가한다. 4대강 하구에 속하는 한 하구의 생물다양성이 한 등급 상승하면 1,519억원(95% 신뢰수준 990억원~2,186억원)의 가치가 증가한다. 그러므로 4대강 하구에 속하는 한 하구가 인공이 아닌 자연 하구이면서 하구 하천 수질이 좋은 수질(2급수) 수준, 하구 해수역 수질이 좋은 수질(1등급), 생물다양성이 높은 수준이면, 경제적 가치는 2조 1,970억원이며 95% 신뢰수준은 1조 7,210억원~2조 8,799억원으로 평가된다.

수도권 통행 특성을 고려한 통행시간가치 산정 연구 (Calculation of Travel Time Values in Seoul Metropolitan Area Considering Unique Travel Patterns)

  • 김경현;이장호;윤일수
    • 대한교통학회지
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    • 제35권6호
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    • pp.481-498
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    • 2017
  • 교통시설 투자사업에 대한 타당성조사 시 가장 큰 비율을 차지하는 편익항목은 통행시간 절감편익이며, 이는 통행시간가치를 이용하여 산정한다. 현재 예비타당성조사 표준 지침(5판)에서는 1999년 전국 지역 간 통행 조사 자료를 기반으로 산정된 업무통행 대비 비업무통행 통행시간가치의 비율을 이용하여 비업무통행 통행에 대한 시간가치를 산정하였으며, 여기에 수도권 통행목적 비율과 재차인원을 적용하여 수도권에 대한 통행시간가치를 산정하였다. 수도권 통행은 전국 지역 간 통행과 다른 통행특성을 가지고 있다. 수도권 통행의 경우 복합 대중교통 수단을 이용한 환승이 빈번하게 발생하고 있으며, 통근통행에 장시간을 소요하고 있다. 따라서 본 연구에서는 타당성조사 관련 지침의 통행시간가치 산정방법을 개선함으로써 수도권의 통행 특성을 반영한 통행시간가치를 산정하였다. 수도권 통행 특성 반영을 위하여 기존 비업무통행에 포함된 통근통행을 분리하여 통근통행에 대한 통행시간 가치를 별도로 산정하였다. 통근통행 모형과 비업무 통행 모형에 대한 우도비 검정통계량 검정 결과 두 모형은 통계적으로 유의미한 차이가 있는 것으로 분석되었다. 또한 수도권 통합요금제 시행에 따른 통행 여건을 반영하기 위하여 대중교통 통합 모형을 구축하였다. 대중교통 통합모형의 버스와 지하철의 계수 비교결과 두 수단간 계수는 통계적으로 유의미한 차이가 없는 것으로 분석되었다.

다변량 프로빗 모형을 이용한 가전제품 구매의 상관관계 분석 (Correlation among Ownership of Home Appliances Using Multivariate Probit Model)

  • 김창섭;신정우;이미숙;이종수
    • 마케팅과학연구
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    • 제19권2호
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    • pp.17-26
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    • 2009
  • As the lifestyle of consumers changes and the need for various products increases, new products are being developed in the market. Each household owns various home appliances which are purchased through the choice of a decision maker. These appliances include not only large-sized products such as TV, refrigerator, and washing machine, but also small-sized products such as microwave oven and air cleaner. There exists latent correlation among possession of home appliances, even though they are purchased independently. The purpose of this research is to analyze the effect of demographic factors on the purchase and possession of each home appliances, and to derive some relationships among various appliances. To achieve this purpose, the present status on the possession of each home appliances are investigated through consumer survey data on the electric and energy product. And a multivariate probit(MVP) model is applied for the empirical analysis. From the estimation results, some appliances show a substitutive or complementary pattern as expected, while others which look apparently unrelated have correlation by co-incidence. This research has several advantages compared to previous literatures on home appliances. First, this research focuses on the various products which are purchased by each household, while previous researches such as Matsukawa and Ito(1998) and Yoon(2007) focus just on a particular product. Second, the methodology of this research can consider a choice process of each product and correlation among products simultaneously. Lastly, this research can analyze not only a substitutive or complementary relationship in the same category, but also the correlation among products in the different categories. As the data on the possession of home appliances in each household has a characteristic of multiple choice, not a single choice, a MVP model are used for the empirical analysis. A MVP model is derived from a random utility model, and has an advantage compared to a multinomial logit model in that correlation among error terms can be derive(Manchanda et al., 1999; Edwards and Allenby, 2003). It is assumed that the error term has a normal distribution with zero mean and variance-covariance matrix ${\Omega}$. Hence, the sign and value of correlation coefficients means the relationship between two alternatives(Manchanda et al., 1999). This research uses the data of 'TEMEP Household ICT/Energy Survey (THIES) 2008' which is conducted by Technology Management, Economics and Policy Program in Seoul National University. The empirical analysis of this research is accomplished in two steps. First, a MVP model with demographic variables is estimated to analyze the effect of the characteristics of household on the purchase of each home appliances. In this research, some variables such as education level, region, size of family, average income, type of house are considered. Second, a MVP model excluding demographic variables is estimated to analyze the correlation among each home appliances. According to the estimation results of variance-covariance matrix, each households tend to own some appliances such as washing machine-refrigerator-cleaner-microwave oven, and air conditioner-dish washer-washing machine and so on. On the other hand, several products such as analog braun tube TV-digital braun tube TV and desktop PC-portable PC show a substitutive pattern. Lastly, the correlation map of home appliances are derived using multi-dimensional scaling(MDS) method based on the result of variance-covariance matrix. This research can provide significant implications for the firm's marketing strategies such as bundling, pricing, display and so on. In addition, this research can provide significant information for the development of convergence products and related technologies. A convergence product can decrease its market uncertainty, if two products which consumers tend to purchase together are integrated into it. The results of this research are more meaningful because it is based on the possession status of each household through the survey data.

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