There is an R package called foretell that is useful for projecting customer retention based on Beta Geometric and Beta Discrete Weibull models.

I am having trouble finding something similar for python, at least one as streamlined. Does anyone know of anything that comes to mind


1 Answer 1


The functions in the foretell package are fairly simple calls to the R optim function with some data management in between. So in R if you run library(foretell);BdW you can see the function definition.

In python, you would just rewrite the R optim call using scipy minimize. Here is a brief example of minimizing the same example in the foretell docs for the BdW model:

from scipy.optimize import minimize
from scipy.special import beta
import numpy as np

surv = np.array([100,86.9,74.3,65.3,59.3])
h = 6
t = len(surv)
die = np.diff(-surv)
i = np.arange(0,t) 

def dbw_ll(x):
    a,b,c = x
    s = beta(a,b + i**c)/beta(a,b)
    p = np.diff(-s)
    ll_ = die * np.log(p)
    ll = ll_.sum() + surv[-1]*np.log(s[-1])
    return -ll

bnds = [(0.001,10000)]*3

res = minimize(dbw_ll, x0=[1,1,1], 

# R results 0.2593549 1.7226948 1.5842688 
# agrees for 3 decimals

# projecting out
a, b, c = res.x
k = np.arange(0,t+h)
dbw = (beta(a,b+k**c)/beta(a,b))*100
fitted = dbw[0:t]
projected = dbw[t:]

It is mostly the same exercise for the other functions (mapping R functions to python). You just need to do a days worth of work to wrap these up in nice functions in python to replicate the same functionality in the R foretell library. (Did this example while waiting for a few queries to finish!)

  • $\begingroup$ Thank you very much for your response. I don't have access to R itself but found said documentation here: rdrr.io/cran/foretell/src/R/BdW.R I suppose I asked this question poorly as I was looking for the model's projection of what retention should be over a certain period. I Think I found that formula here : dbw <- (beta(a, b+(k^c)) / beta(a, b))*100 With the results we printed in your answer (res.x), how would I go about inputting that to predict retention at time = 6? $\endgroup$
    – Kbbm
    Jun 9, 2021 at 21:56
  • $\begingroup$ Ahhh, I figured it out. In this example it would go as: dbw = (sc.beta(0.2593549, 1.7226948 + (5**1.5842690)) / sc.beta(0.2593549, 1.7226948))*100,, which will return 54.66. $\endgroup$
    – Kbbm
    Jun 9, 2021 at 22:17
  • 1
    $\begingroup$ You got it @KyleMcComb, added a few more lines to show how to generate the projected values (again pretty similar between R/python, so not that much work to translate). $\endgroup$
    – Andy W
    Jun 10, 2021 at 11:30

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