Uncertain Bass diffusion model and modeling the purchase volume of private cargo vehicles in China

For forecasting the spread of new goods and technology, the Bass diffusion model is an extremely important model. While this model fully considers the product life cycle, it lacks a comprehensive consideration of uncertain factors that influence products and customers’ demand. In many cases, describing these uncertain factors as stochastic processes in an approach may lead to certain issues. Therefore, in this paper, we put forward an uncertain Bass diffusion model integrating uncertainty theory. Based on this model, the properties of the $\alpha$-path, uncertainty distribution, and inverse uncertainty distribution of the solution to the uncertain Bass diffusion model are studied. Second, the unknown parameters in the uncertain Bass diffusion model are estimated using the method of moments. Then, within the scope of uncertainty theory, we use uncertainty hypothesis test to evaluate whether the observed data conform to the specified uncertainty distribution, and to test whether the parameter estimation method is rational and valid. Finally, we carry out a numerical simulation on the purchase volume of private cargo vehicles in China by using uncertain differential equations and stochastic differential equations. The results show that modeling with uncertain differential equations is superior to using stochastic differential equations.