Contrasting the two fundamental approaches to valuing customers: Contractual (Subscription) vs. Non-Contractual (Retail).
Customer Profile
New CustomerLoyal
12 months
This is "s" in P(T > t+s | T > s)
$50
StickyHigh Risk
3.0% / mo
The "Reset" Logic
In the Telco model, if a customer has already survived 12 months, we reset the clock. We only care about the probability of them surviving future months given they are here today.
Survival Probabilities (Exponential)
Discounted Expected Value (Accumulated)
Formula:
CLV = ∑ [ S(t + s | T > s) × $M × (1+d)-t ]
BG/NBD Model— P(Alive) and E[Tx] use the closed-form BG/NBD equations from Fader, Hardie & Lee (2005). Hyperparameters (r, α, a, b) are assumed known; in production these would be estimated via maximum likelihood on your transaction log.
RFM Inputs
Weeks since first purchase
52 weeks
Weeks since first purchase
40 weeks
Warning: High gap!
Total repeat purchases
5 purchases
The "Ghost" Logic
We don't know if they left. The BG/NBD model combines Recency, Frequency, and T with population-level hyperparameters to compute the posterior probability that a customer is still active.
Advanced: BG/NBD Hyperparameters
In production, these are estimated via MLE on your full transaction log. Here you can set them manually to explore model behavior.
0.25
4.00
0.80
2.50
Customer Timeline (Buy 'Til You Die)
P(Alive)
0%
Prob. active right now (BG/NBD closed-form)
Est. Future Tx
0.00
over next 12 weeks (BG/NBD conditional expectation)
User-defined input
Est. 12-Week Customer Value
$0.00
E[Tx] × Avg Spend
P(Alive) Decay If The Silence Continues
Holding the purchase history fixed, this shows how the model's belief that the customer is still active erodes with each additional week of silence.