Abstract: The structure of the classical Bass diffusion model reveals that the maximum number of imitators is achieved when the cumulative number of adopters equals half the maximum number of adopters in the market. But this situation does not necessarily correspond to the actual activities. To more accurately represent where the number of imitators reaches its peak, a new grey Bass diffusion model for cases with small samples is proposed by introducing a parameter to the classical Bass diffusion model to improve the model. In addition, the solution of the grey Bass diffusion model is derived by integrating the grey Bass diffusion model representation, and the parameter-solving process of the new grey Bass diffusion model is given by using the ordinary least squares method. Finally, an example of new energy vehicle sales forecasting shows that the new grey Bass diffusion model is more accurate than the traditional grey Bass diffusion model. The new grey Bass diffusion model further broadens the use of the Bass diffusion models and enriches the mathematical methods of innovation diffusion.

Key words: Bass Diffusion Model, Extended Grey Bass Diffusion Model, Innovation Diffusion, Ordinary Least Squares