expected_customer_lifetime_value returns NaN for large customers / long horizons (BG/NBD + Gamma-Gamma)

[haseeb1431]

Hi,

I’m fitting a BetaGeoModel + GammaGammaModel for different size of customer datasets we calculate CLV projections over 10 to 15 years. It has been working fine until we got a dataset where we start to get NaN for CLV. Everything looks fine for short horizons (1–3 years), but when I call expected_customer_lifetime_value with longer horizons (≥ 4–5 years) I start getting NaN CLV values for some customers.

As I understood, it was happening due to larger monetary values so I have tried to use lograthmic or scaled down the values but still continue to get null CLV values. The following is a sample output for a scaled down monetary value.
Example output:

customer_id	frequency	recency	T	monetary_value	clv_for_1_years	clv_for_2_years	clv_for_3_years	clv_for_4_years
13	704	1457	1457	236.39	37368.35	69637.69	97629.66	121989.7
16	646	1456	1456	816.39	118507.86	220845.04	309617.25	386871.38
27	1087	1456	1457	7060.22	1720000	3210000	4500000	NaN

Observations:

Scaling monetary_value helps avoid immediate overflow, but NaN still appears for high-frequency/high-spend customers after a few years. Looks like the closed-form expectation formula inside expected_customer_lifetime_value overflows with extreme parameter/posterior values, even though a Monte Carlo simulation would still yield finite numbers.

Steps to Reproduce

from pymc_marketing import clv

# Fit BG/NBD
bgm = clv.BetaGeoModel(data=rfm_data)
idata_bgm = bgm.fit(fit_method="mcmc", draws=1000, tune=1000, target_accept=0.93)

# Fit Gamma-Gamma (scaled monetary_value)
ggm = clv.GammaGammaModel(data=nonzero_data)
idata_ggm = ggm.fit(fit_method="mcmc", draws=1000, tune=1000, target_accept=0.93)

# Compute CLV
clv = ggm.expected_customer_lifetime_value(
    transaction_model=bgm,
    data=nonzero_data,
    future_t=120,                # 10 years
    discount_rate=0.01,
    time_unit="month"
)
print(clv.to_dataframe().head())

Expected behavior

Return finite (though large) CLV values, even for high-frequency / high-spend customers. At minimum, gracefully warn about overflow instead of returning NaN.

Questions

• What are the different techniques I can try to calculate the CLV for larger clients?