A Negative Binomial model for the donations count in Fundraising Management

Forecasting expected gifts is a key task in Fundraising Management. In this study, we propose modeling a gift as an individual risk that can be analyzed from multiple perspectives: the occurrence, frequency, and timing of donations, as well as their monetary amounts. We focus specifically on modeling the number of donations as a Poisson random variable whose intensity parameter depends on individual donor characteristics. By introducing a Gamma-distributed heterogeneity factor, a Negative Binomial model arises as a natural extension of the starting framework. This approach enables the estimation of both the expected number of donations and the probability of a gift through Negative Binomial regression. We illustrate the methodology with an empirical application.