Let’s say that you have a service up for subscription. Customers love your product, they roll in to register and renew their subscription each month. But not all, some of them stop.

In this post, I describe the Beta-Geometric model for modelling such behavior. We assume that the customer churns at a constant rate p. Then the probability that the customer churn at exact month k is . This is the Geometric distribution. We also do not know much about p itself, only that p is in the range of [0,1]. For p, we place a Beta distribution over it. We got ourselves the Beta-Geometric model of churn.

The casual way for us to infer p from a dataset with maximum likelihood, like this.

But we’re not so casual now, are we ? As we care also about the uncertainty of our estimates. In this notebook, I demonstrate such a model on a synthetic dataset and prove that we can model such a business process and some more.

Not only that we can find out the distribution of churn rates, we can track it over time and make inference on the churn behavior of our customers.

Notebook