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Bass diffusion model : ウィキペディア英語版
Bass diffusion model
The Bass Model or Bass Diffusion Model was developed by Frank Bass and it consists of a simple differential equation that describes the process of how new products get adopted in a population. The model presents a rationale of how current adopters and potential adopters of a new product interact. The basic premise of the model is that adopters can be classified as innovators or as imitators and the speed and timing of adoption depends on their degree of innovativeness and the degree of imitation among adopters. The Bass model has been widely used in forecasting, especially new products' sales forecasting and technology forecasting. Mathematically, the basic Bass diffusion is a Riccati equation with constant coefficients.
Frank Bass published his paper "A new product growth for model consumer durables" in 1969 whose title indeed contained a typographical error. Prior to this, Everett Rogers published ''Diffusion of Innovations'', a highly influential work that described the different stages of product adoption. Bass contributed some mathematical ideas to the concept.〔''Management Science'' 50 Number 12 Supplement, Dec 2004 ISSN 0025-1909 p1833-1840〕
==Model formulation==

:\frac = p + q F(t)
Where:
* \ f(t) is the change of the installed base fraction
* \ F(t) is the installed base fraction
* \ p is the coefficient of innovation
* \ q is the coefficient of imitation
Sales \ S(t) is the rate of change of installed base (i.e. adoption) \ f(t) multiplied by the ultimate market potential \ m :
:\ S(t)=mf(t)
:\ S(t)=m} \frace^)^2}
The time of peak sales \ t^
*
: \ t^
*=\frac 〔

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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