销售扩散曲线及其数学分析  

The Mathematical Analysis of Sales Diffusion Processes

作　　者：郑祖康[1] 

机构地区：[1]复旦大学管理学院,上海200433

出　　处：《数学理论与应用》2010年第3期1-12,共12页Mathematical Theory and Applications

摘　　要：本文利用概率分布函数来描述销售扩散过程,面对到目前为止的销售扩散曲线,消费者、技术人员和销售人员会有一种"冲动",正是这种"冲动"推动了销售扩散曲线下一步的发展。这种"冲动"可以用统计中生存分析的方法给以描述。我们把这种"冲动"分别与当前的销售扩散曲线、平均销售扩散速度和销售时间联系起来,在数学上构成三类微分方程。利用这些微分方程的解,可以预测出销售最高峰、销售量过50%的时间等。We consider a sales diffusion process as a probability function. Face at a sales diffusion curve so far, there is an ＂impulse＂ of the consumers, the sales people and the technicians, which push the sales diffusion process to advance. We link the ＂impulse＂, which is described by the method of survival analysis in statistics, to the current diffusion curve, the average rate and sales time respectively. The linkage constructs three types of differential equa- tions in mathematics. From these solutions, we can do some predictions, for example the time point the sales get the maximum, or the time point that 50% consumers of the target group buy the new products etc.

关 键 词：销售扩散过程 生存分析 概率分布函数 微分方程 

分 类 号：F274[经济管理—企业管理]