The authors present a general framework for purchase frequency modelin
g that enables flexible fitting and convenient computation. Their easi
ly described purchase frequency distributions subsume many previous mo
dels and provide a connection between mixed Poisson marketing models a
nd the conceptually distinct compound Poisson models. These distributi
ons provide simple parametric equations for individual-level predictio
n of second-period purchase frequency based on observed first-period p
urchase frequencies. The results are applied to four marketing panel d
ata sets.