I am looking at implementing a Pareto/NBD model to forecast customer lifetime value in a non-contractual business setting. One thing I haven't got my head around yet is whether such a model is equally applicable to both new and existing customers.
Our revenue model works as follows: first, the customer pays a signup fee to open an account (in some cases this is free, but that's probably besides the point for this discussion); following that, the customer will make as many transactions as they like (some revenue-generating, others not) until they "die", but given it's a buy-till-you-die model, we have no definitive indicator of churn, hence the need for such a model. I would consider the initial signup to be the "first purchase", with all further transactions counting as "repeat purchases", the latter being the behaviour that Pareto/NBD seeks to model.
Let's say I took a calibration period of 8 weeks. For existing customers (already using the product prior to the beginning of the calibration period), I assume the "first purchase" would simply be the first transaction they make within that calibration period, even though - in reality - that's a repeat purchase in the sense that they already made their first purchase prior to the calibration period. I have seen the T variable in the CBS referred to as the "age of the customer", but given that the calibration period does not necessarily contain the customer's full customer lifetime to date, presumably this is misleading and should be understood as "time from first purchase to end of calibration period"?
The seemingly tricky thing from my perspective is whether it's reasonable to treat repeat purchases following signup (for new customers) the same as repeat purchases following the first transaction in the calibration period (for existing customers), given the time between first and repeat purchase (and likelihood of "death") will almost certainly differ between those two cases.
Has anybody dealt with a similar case before, or can offer any guidance?