https://github.com/jdmaturen/shifted_beta_geometric_py

An implementation of the shifted-beta-geometric (sBG) model from Fader and Hardie's "How to Project Customer Retention" (2006)
https://github.com/jdmaturen/shifted_beta_geometric_py

customer-retention fader hardie numpy python sbg scipy

Last synced: about 2 months ago
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An implementation of the shifted-beta-geometric (sBG) model from Fader and Hardie's "How to Project Customer Retention" (2006)

• Host: GitHub
• URL: https://github.com/jdmaturen/shifted_beta_geometric_py
• Owner: jdmaturen
• License: apache-2.0
• Created: 2013-10-14T17:39:05.000Z (about 11 years ago)
• Default Branch: master
• Last Pushed: 2020-10-25T00:27:05.000Z (about 4 years ago)
• Last Synced: 2024-10-31T08:42:04.892Z (about 2 months ago)
• Topics: customer-retention, fader, hardie, numpy, python, sbg, scipy
• Language: Python
• Size: 121 KB
• Stars: 56
• Watchers: 2
• Forks: 21
• Open Issues: 4
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# 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)](http://www.brucehardie.com/papers/021/sbg_2006-05-30.pdf).

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)](https://marketing.wharton.upenn.edu/files/?whdmsaction=public:main.file&fileID=341)

## Example

```python

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.