A discrete innovation diffusion model incorporating change in the adoption rate

摘要

New products play a significant role in the success of firms concerned with the introduction of innovative products. Mathematical modeling that can describe the life cycle of these products can provide major contribution in their successful diffusion. The Bass model of innovation diffusion is a main representative of the diffusion models. Many modifications have been made to the model since its development to answer the changing needs and limitations. The model was developed in continuous time, which limits its application on many real life applications having discrete time data. Due to this reason a discrete version of this model was proposed by another author Hirota. The model was based on Riccati's equation in mathematics. Although the model can be solved to exact solution but it is difficult to modify this model further and solve to get the exact solution. Further, in practice the pace of diffusion varies not only because of the life cycle phase but due to many other variations such as changes in advertising strategies, little product modifications, competitive products etc. In marketing this concept can be termed as change point. In the present article, we propose an approach to model the diffusion process using a discrete logistic function whose exact solution can be obtained using probability generating function (PGF), incorporating the aforesaid change point concept. The model is validated on the real life data sets. Therefore, the proposed model provides accurate parameter estimates, making it possible to predict when a product can be launched.