A stochastic approach to diffusion model with asymmetric influence. (1st January 2011)

• Record Type: Journal Article
• Authors: Suzuki, Naomichi; Tanaka, Masatoshi; Kasai, Kazuhiro; Sung, Kijung
• Is Part Of: International journal of manufacturing technology and management. Volume 22:Number 1(2011)
• Page Start: 78
• Page End: 92
• Publication Date: 2011-01-01
• Subjects: diffusion model -- asymmetric influence -- birth and death process -- bass model; Manufacturing processes -- Periodicals; Manufacturing processes -- Automation -- Periodicals; Production management -- Periodicals; 670.427068
• Languages: English
• ISSNs: 1368-2148

Abstract

A diffusion model with innovators and imitators is formulated by the use of the generalised birth process with immigration. In our formulation, the immigration rate and the birth rate have time dependence. The immigration process corresponds to the behaviour of innovators and the birth process to that of imitators. The Bass model is derived under the assumption that the ratio of the immigration rate to the birth rate is constant. An extension of the Bass model based on the stochastic process is proposed, by which data with broad peak or bimodal shape can be analysed. Data on the sales of new products and on hit phenomena are analysed by the diffusion model.