The Gamma/Weibull Customer Lifetime Model
Gen Ye , Songjian Wang
Communications in Mathematics and Statistics ›› 2019, Vol. 7 ›› Issue (1) : 33 -59.
The Gamma/Weibull Customer Lifetime Model
This paper proposes a new customer lifetime model: the Gamma/Weibull distribution (G/W). Similar to the Pareto/NBD model, we propose a G/W/NBD model by combining the G/W distribution with a negative binomial distribution (NBD) and study its properties such as (i) the probability that a customer to be alive at a time point; (ii) the expectation and variance of the number of transactions for a customer during a fixed time period; (iii) the conditional expectation and conditional variance of the number of future transactions for a customer during a fixed time period. Several simulation studies are conducted to investigate the forecasting accuracy and flexibility of the proposed model. A CDNOW data set is analyzed by the proposed model.
Customer lifetime / Gamma distribution / Negative binomial distribution / Purchase history / Weibull distribution
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