# A generalized Bayesian framework for the analysis of subscription based businesses

## TL;DR

This paper introduces a Bayesian framework for analyzing subscription businesses using a unified metric called SCV, modeling customer churn as an exponential decay, and providing closed-form solutions for revenue estimation.

## Contribution

It presents a novel Bayesian probabilistic model for subscription analysis, including exact and approximate solutions for churn modeling and a methodology for decision making.

## Key findings

- Closed-form solution for constant churn model
- Approximate solution for exponential decay churn model
- Case study demonstrating practical application

## Abstract

We have created a framework for analyzing subscription based businesses in terms of a unified metric which we call SCV (single customer value). The major advance in this paper is to model customer churn as an exponential decay variable, which directly follows from experimental data relating to subscription based businesses. This Bayesian probabilistic model was used to compute an expected value for the revenue contribution of a single user. We obtain an exact closed-form solution for the constant churn model, and an approximate closed-form solution for the exponential decay model. In addition, we define a general methodology for decision making processes using sensitivity analysis of the model equation, which we illustrate with a real-life case study for a food based subscription business.