Calculating probability of churn time from interaction intervals How can I calculate the probability, that customers of an online shop are most likely churned (not coming back), given their interaction histories.
In detail, the histories include only timestamps of interactions. As an example, we know 


*

*Customer A interacted with a shop at 1st of March, 4 days later, and again 10 days later, and hasn't been seen again since then

*Customer B interacted at 1st of April, and then regularly every 4-6 days

*Customer C interacted only once with the shop at April 15th 


Can I compute from this kind of data after how much time it is very likely (lets say 90% probability) that customers will NOT come back to the shop? I do not want to include interaction types and similar information.
EDIT:
After some more consideration, my current approach is, to take the longest time that a customer took to come back to the shop (lets call it comeback-time). Now I can compute the comeback-time at which 90% of the users are below it, and assume, that after that, they are usually not coming back.
However, I'm not particularly happy with that approximation, since some users could have been away for very long times for a single time. Also, using the maximum is ignoring a huge part of the information in the data set. I would be glad for other approaches.
 A: What you are looking for are recurrent-events survival analysis models. In general, survival analysis models are estimating the survival function, i.e. $S(t) = \Pr(T > t)$ (e.g. number of years till death, hence the "survival analysis" name). The recurrent-events models extend classical survival analysis models to data with multiple re-occuring events (e.g. relapses of some disease). In your case events are visits in shops and the "survival time" is the churn time. You can find some friendly introduction on such models e.g. in Modelling recurrent events: a tutorial for analysis in epidemiology paper by Amorim and Cai (2005) that also reviews the available software for estimating such models.
A: To use the information you have, you can create a classifier whether it is the last visit or not. A recurrent neural network may be a very good choice.
Input data: sequences of times of visit.
Output data: was/wasn't it the last visit.
Having that classifier, you can examine e.g. the ROC or precision-recall curves and set the threshold according to your expectations.
