• Asia Marketing Journal
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• v.11 no.1
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• pp.29-38
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• 2009

Estimating the Bass diffusion model often creates a time-interval bias, which leads the OLS approach to overestimate sales at early stages and underestimate sales after the peak. Further, a specification error from omitted variables might raise serial correlations among residuals when marketing actions are not incorporated into the diffusion model. Autocorrelated disturbances may yield unbiased but inefficient estimation, and therefore invalid inference results. This phenomenon warrants a modified approach to estimating the Bass diffusion model. In this paper, the authors propose a modified Bass diffusion model handling autocorrelated disturbances. To validate the new approach, authors applied the method on two different data-sets: CT Scanners in the U.S, and FPD TV sales in Korea. The results showed improved model fit and the validity of the proposed model.

• Journal of Energy Engineering
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• v.17 no.1
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• pp.31-37
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• 2008

At present, the target amount of demand-side management and investment cost of EE (Energy Efficiency) program, which consists of high-efficiency appliances, has been estimated simply by the diffusion function based on the real historical data in the past or last year. In the internal and external condition, the penetration amount of each appliance has been estimated by Bass diffusion model which is expressed by time and three coefficients. And enough acquisition of real historical data is necessary for reasonable estimation of coefficients. In energy efficiency, to estimate the target amount of demand-side management, the penetration amount of each appliance should be primarily forecasted by Bass diffusion model in Korea. On going programs, however, lightings, inverters, vending machine and motors have a insufficient real historical data which is a essential condition to forecast the penetration amount using a Bass diffusion model due to the short period of program progress. In other words, the forecast of penetration amount may not be exact, so that it is necessary for the method of forecast to apply improvement of method. In this paper, the penetration amount of high-efficiency appliances is forecasted by Bass, virtual Bass, Logistic and Lawrence & Lawton diffusion models to analyze the diffusion progress. And also, by statistic standards, each penetration is compared with historical data for model suitability by characteristic of each appliance. Based on the these result, in the forecast of penetration amount by diffusion model, the reason for error occurrence caused by simple application of diffusion model and preferences of each diffusion model far a characteristic of data are analyzed.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.11a
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• pp.413-416
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• 2006

신제품이나 서비스의 수요 예측을 Bass 확산 모형을 토대로 수행할 때의 가장 큰 문제점은모형의 파라미터 추정에 필요한 데이터가 충분치 않다는 것이다. 따라서 Bass 확산 모형의 핵심적인 두 파라미터인 혁신 계수(p)와 모방 계수(q)의 추정을 시도할 때, 어느 정도의 데이터 개수가 요구되는 지를 파악하는 것은 매우 현실적인 중요성을 갖는 문제이다. 이제까지의 연구는 주로 기존의 판매 데이터를 토대로 Bass 모형의 파라미터를 추정할 때, 생기는 다양한 문제점 파악에 집중되었다. 시뮬레이션의 경우는 Bass 모형에 랜덤 오차를 추가하여 실시하였다. 이 경우 데이터 개수가 계수추정에 미치는 영향은 도출되나 각 계수별 민감도 분석이 제대로 이루어지지 못하는 한계를 가지고 있다, 따라서 본 논문에서는 시뮬레이션에서 예측치를 발생시킬 때 랜덤 오차 대신, 혁신 계수와 확산 계수의 변동을 주는 방법을 도입한다. 결과는 다음과 같다. 첫째, p 변동보다는 q 변동이 예측치의 오차에 대해 보다 중요하다. 둘째, 오차가 잠재수요의 30%이하로 떨어지기 위해서는 수요가 최대로 도달하는 시점이 $t^*$ 일 경우, $t^*\;+1$까지 데이터가 요구된다.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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• pp.1089-1094
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• 2005

Peterson and Mahajan(1978)은 Bass모형을 확장한 종속적 신상품 수요확산모형(contingent diffusion model)을 처음으로 제안하였다. Peterson and Mahajan(1978)이 명명한 상품간의 종속적(contingent) 관계란, 주 상품의 경우는 다른 상품에 독립적이지만 종속적 상품(contingent product)의 경우는 잠재시장이 주 상품의 누적 구매자 수에 의존하는 경우를 말한다. 그런데 Peterson and Mahajan이 제안한 기존 모형은 실질적 활용에 있어서 모형 추정이 불가능하다는 단점을 지니고 있을 뿐만 아니라, Bass(1969) 모형처럼 엄밀한 확률이론에 근간을 둔 모형이라기보다는 직관과 통찰력에 근간을 둔 Bass모형의 단순한 확장 모형이라는 한계를 지니고 있다. 본 연구는 이러한 한계를 극복하고 확률이론을 바탕으로 종속적 관계를 가지는 상품들에 대한 수요 확산모형을 개발하는데 목적이 있다. Bass의 신상품확산모형은 hazard 함수 모형의 일종으로 신상품의 확산을 혁신과 구전효과로 설명한 과학적 모형이다. 본 연구에서는 확률이론을 활용함으로써 이러한 Bass의 hazard 함수 모형의 확장이 가능함을 보이고, 이를 토대로 종속적 관계에 있는 신상품들에 대한 수요 확산모형을 개발하였다. 또한 개발된 모형을 한국의 이동전화와 무선인터넷 사례에 적용하여 실증 분석을 수행하였다.

• Asia Marketing Journal
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• v.3 no.3
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• pp.46-70
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• 2001

본 연구는 첨단기술 제품들에서 볼 수 있는 지속적인 기술혁신으로 인하여 새롭게 시장에 진입하는 신규세대 제품과 이전세대 제품들의 동태적 판매량을 묘사하고 예측할 수 있는 모형들을 제시하고 비교·분석하는데 목적이 있다. 본 논문에서는 Bass(1969)의 내구성 소비재에 대한 최초구매 확산모형을 기반으로 하여 개발된 기술적 대체를 반영한 확산모형들, 즉 Norton and Bass(1987), Mahajan and Muller(1996), Jun and Park(1999)의 모형들의 이론적인 틀과 가정들을 비교·분석함으로써 기존 모형과는 변수와 계수의 의미가 다른 모형을 제시하고, 전세계 DRAM 반도체 출하량 자료를 사용하여 모형들 간의 경험적 비교를 행하였다. Jun and Park(1999)이 전세계 DRAM 반도체 출하량 자료에 적용하기 위하여 새롭게 개발한 타입 II 모형(즉 JP2)은 본 연구의 경험적 비교의 결과에 비추어 볼 때 그들의 타입 I 모형이 취한 가정들을 변화시켜서 모형을 구성하는 변수들과 계수들의 의미가 달라진 JPI 모형 또는 Norton and Bass(1987)의 모형(즉 NB1)보다 실제 적용에 있어서 열등할 수 있다는 것을 본 연구는 보여주었다.

• Journal of Digital Convergence
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• v.12 no.3
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• pp.141-147
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• 2014

Diffusion model is popular research topic in marketing and economy particularly for the areas of model specification and market size forecasting. In particular, Bass model can explain Roger's innovation diffusion and product life cycle through easy mathematical representation and hence the model has been widely used for the explanation of adopting innovative new products and technologies. Nonetheless, there're only a couple of pioneering researches about semiconductor market, using diffusion models. Consequently, we'd utilise NLS approach diffusion model to estimate the market potential of MOSFET, major switching device for power management of system, and explain the process to industry stakeholders and policy makers for delivery of managerial implication with pragmatic purpose.

• The Korean Journal of Applied Statistics
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• v.14 no.2
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• pp.233-243
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• 2001

중장기 수요예측을 위해 자주 사용되는 방법으로 확산모형과 성장곡선모형을 들 수 있다. 본 논문에서는 이들 방법론의 성격 및 실제 적용에 있어 모수추정에 따른 문제점들을 살펴보고, 모수추정을 효율적으로 수행하기 위한 전략을 제시한다. 또한 실제 자료에 각 방법론들을 적용하여 예측결과를 비교한다.

• ETRI Journal
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• v.10 no.1
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• pp.39-52
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• 1988

This study suggests the diffusion models to predict the spread pattern of telecommunications services. The extended models containing both (either) price and (or) income varible are offered on the basis of Bass model. At the empirical test using Korean telephone data, the models with either price or income varible are the best forecasting model under apriori selected econometric criteria.

• Journal of Distribution Research
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• v.15 no.4
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• pp.61-85
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• 2010

Introduction: Diffusion is process by which an innovation is communicated through certain channel overtime among the members of a social system(Rogers 1983). Bass(1969) suggested the Bass model describing diffusion process. The Bass model assumes potential adopters of innovation are influenced by mass-media and word-of-mouth from communication with previous adopters. Various expansions of the Bass model have been conducted. Some of them proposed a third factor affecting diffusion. Others proposed multinational diffusion model and it stressed interactive effect on diffusion among several countries. We add a spatial factor in the Bass model as a third communication factor. Because of situation where we can not control the interaction between markets, we need to consider that diffusion within certain market can be influenced by diffusion in contiguous market. The process that certain type of retail extends is a result that particular market can be described by the retail life cycle. Diffusion of retail has pattern following three phases of spatial diffusion: adoption of innovation happens in near the diffusion center first, spreads to the vicinity of the diffusing center and then adoption of innovation is completed in peripheral areas in saturation stage. So we expect spatial effect to be important to describe diffusion of domestic discount store. We define a spatial diffusion model using multinational diffusion model and apply it to the diffusion of discount store. Modeling: In this paper, we define a spatial diffusion model and apply it to the diffusion of discount store. To define a spatial diffusion model, we expand learning model(Kumar and Krishnan 2002) and separate diffusion process in diffusion center(market A) from diffusion process in the vicinity of the diffusing center(market B). The proposed spatial diffusion model is shown in equation (1a) and (1b). Equation (1a) is the diffusion process in diffusion center and equation (1b) is one in the vicinity of the diffusing center. $$\array{{S_{i,t}=(p_i+q_i{\frac{Y_{i,t-1}}{m_i}})(m_i-Y_{i,t-1})\;i{\in}\{1,{\cdots},I\}\;(1a)}\\{S_{j,t}=(p_j+q_j{\frac{Y_{j,t-1}}{m_i}}+{\sum\limits_{i=1}^I}{\gamma}_{ij}{\frac{Y_{i,t-1}}{m_i}})(m_j-Y_{j,t-1})\;i{\in}\{1,{\cdots},I\},\;j{\in}\{I+1,{\cdots},I+J\}\;(1b)}}$$ We rise two research questions. (1) The proposed spatial diffusion model is more effective than the Bass model to describe the diffusion of discount stores. (2) The more similar retail environment of diffusing center with that of the vicinity of the contiguous market is, the larger spatial effect of diffusing center on diffusion of the vicinity of the contiguous market is. To examine above two questions, we adopt the Bass model to estimate diffusion of discount store first. Next spatial diffusion model where spatial factor is added to the Bass model is used to estimate it. Finally by comparing Bass model with spatial diffusion model, we try to find out which model describes diffusion of discount store better. In addition, we investigate the relationship between similarity of retail environment(conceptual distance) and spatial factor impact with correlation analysis. Result and Implication: We suggest spatial diffusion model to describe diffusion of discount stores. To examine the proposed spatial diffusion model, 347 domestic discount stores are used and we divide nation into 5 districts, Seoul-Gyeongin(SG), Busan-Gyeongnam(BG), Daegu-Gyeongbuk(DG), Gwan- gju-Jeonla(GJ), Daejeon-Chungcheong(DC), and the result is shown