A MCMC approach for modeling customer lifetime behavior using the COM-Poisson distribution

作者：Ben Mzoughia Mohamed^*; Borle Sharad; Limam Mohamed

来源：Applied Stochastic Models in Business and Industry, 2018, 34(2): 113-127.

DOI：10.1002/asmb.2276

• Conway-Maxwell-Poisson
• customer lifetime transactions
• customer lifetime value
• MCMC
• prediction
• segmentation

One of the major challenges associated with the measurement of customer lifetime value is selecting an appropriate model for predicting customer future transactions. Among such models, the Pareto/negative binomial distribution (Pareto/NBD) is the most prevalent in noncontractual relationships characterized by latent customer defections; ie, defections are not observed by the firm when they happen. However, this model and its applications have some shortcomings. Firstly, a methodological shortcoming is that the Pareto/NBD, like all lifetime transaction models based on statistical distributions, assumes that the number of transactions by a customer follows a Poisson distribution. However, many applications have an empirical distribution that does not fit a Poisson model. Secondly, a computational concern is that the implementation of Pareto/NBD model presents some estimation challenges specifically related to the numerous evaluation of the Gaussian hypergeometric function. Finally, the model provides 4 parameters as output, which is insufficient to link the individual purchasing behavior to socio-demographic information and to predict the behavior of new customers. In this paper, we model a customer's lifetime transactions using the Conway-Maxwell-Poisson distribution, which is a generalization of the Poisson distribution, offering more flexibility and a better fit to real-world discrete data. To estimate parameters, we propose a Markov chain Monte Carlo algorithm, which is easy to implement. Use of this Bayesian paradigm provides individual customer estimates, which help link purchase behavior to socio-demographic characteristics and an opportunity to target individual customers.

• 出版日期2018-4