I've got a significant core population (1.3MM), along with the probability of an event occurring within that population (p of a person making a purchase at a specific store across NA vs. purchases made at any store across NA). Because there are so many stores, the p for any specific merchant is extremely low (<0.1%).

I've also got a defined sample population that is very small and cannot be increased (~50 people). Performing binomial analysis is proving to be too sensitive, because every store in the sample of 50 is well outside the normal population with a single event.

Is there another method that could be used that might be more suitable?

Thanks,

What?? In simple english please.

Binomial does not appear to be the best choice for discrte event analysis when the probability of the event is so low. Is there a more appropriate model?