Heterogeneity in p then is modeled with a beta
distribution, which ensures flexibility and values
between 0 and 1. The beta distribution is gðpja; bÞ ¼
pa1ð1pÞb1
Bða;bÞ : Nevertheless, the probability p of
becoming inactive after any transaction and the
transaction rate k both vary independently across
customers. Fader et al. (2005a) show a link between
dropout probability and date of inactivity s,
Eðsjk; pÞ ¼ 1
kp; which can be considered an effect of
exhaustion.