2010, Vol. 20, Issue 3-4, an item 3
KAPŁON R., Heterogeneity in models of purchase frequency – A comparison of Poisson-gamma mixtures with finite Poisson mixtures
Poisson models are fundamental in the modeling of purchase frequencies. However, very often they are statistically incompatible with the data. This stems from the fact that the mean is assumed to be equal to the variance and, in consequence, this fails to capture heterogeneity. Thus Poisson mixture models are often considered instead. The most commonly used of these models is the Poisson-gamma mixture model, which is very often applied to problems in marketing. Hence, it would be advisable to discover its limitations. Using real marketing data sets, we point out the limitations of this approach. Furthermore, we compare it with finite Poisson mixtures.
Keywords: Poisson mixture models, heterogeneity, purchase frequency