## Repeat Buying Model

In this chapter, the following papers will be explained. More papers will be added as needed.

Dr. Ehrenberg’s famous paper “Repeat-Buying” is one of the most cited papers in “Strategic Theory of Stochastic Trials”. Also, it is no exaggeration to say that all the mathematical backgrounds that have been established in this website are cited from this paper. In this chapter, we will focus on opening the parts necessary to understand the “Strategic Theory of Stochastic Trials”.

### Rationale for using the gamma distribution to represent the long-term average number of purchases

In Dr. Eherenberg’s paper, he does not raise a direct rationale for assuming the gamma distribution. It also clearly states that it is not a strict assumption. It says that it is possible to reproduce the actual data and that it has two variables as fitting parameters.

It is also described in this paper that the negative binomial distribution is derived as a result of the mixture distribution of Poisson and Gamma distributions. The following table is similar to the table discussed in “Strategic Theory of Stochastic Trials”. It is assumed that the author also created the table by referring to this paper.