Some approximations for the moments of a process used in diffusion of new products

We consider approximations for the moments of a well known birth process commonly used in a variety of applications involving diffusion of new products and services. This process also has applications in Epidemiology and Social Sciences. The available approximation for the mean function involves the use of a well known population dynamics model. Direct substitution of this formula in the mean variance relationship leads to an identically zero variance function. We propose an improvement for approximating the mean function. Further, we propose two nontrivial approximations for the variance function. Both of the approximations are evaluated in a limited simulation study. As a extension, the problem of approximating the correlation function is also considered.