sBG model of customer retention

A python implementation of the shifted-beta-geometric (sBG) model from Fader and Hardie's "How to Project Customer Retention" (2006).

Important note to modelers: amongst other presumptions, see §3 of the paper, sBG is only applicable to discrete, contractual customer relationships:

Figure Source: "Probability Models for Customer-Base Analysis" (Fader and Hardie 2009)

Example

from shifted_beta_geometric import derl, fit, predicted_survival

# measured percentage of cohort that survives over time
example_data = [.869, .743, .653, .593, .551, .517, .491]

# fit our observed data to the sBG model, which returns the parameters alpha and beta
alpha, beta = fit(example_data)

# predict the next 5 time samples:
future = predicted_survival(alpha, beta, len(example_data) + 5)[-5:]

# future = [0.460, 0.436, 0.414, 0.395, 0.378]

# compute the discounted expected residual lifetime (DERL) for the survivors
# of this cohort at point in time t:
discount = 0.10  # rate at which we discount future revenue
                 # to get value in today's terms, e.g. 10%/year
t = len(example_data)
residual_cohort_lifetime = derl(alpha, beta, discount, t)

# residual_cohort_lifetime = 7.530

# if our average revenue per period per customer is a constant v_avg,
# to get the residual customer lifetime value (CLV) of this cohort
# we simply multiply the residual_cohort_lifetime by v_avg:

v_avg = 10
residual_cohort_clv = residual_cohort_lifetime * v_avg

# thus residual_cohort_clv = $75.30 per customer in this cohort

Requirements

sBG requires numpy and scipy for fitting and the gauss hypergeometric function.