A Neural Network Extension for Solving the Pareto/Negative Binomial Distribution Model

Abstract

This research proposes a new estimation scheme to solve the estimation burden of the Pareto/NBD model and to release its power in out-of-sample prediction and then builds a neural network-based model (NNA-based model) for parameter estimation of the Pareto/NBD model, by designing a loss function to include the likelihood of the Pareto/NBD model and the mean absolute error. Following empirical analysis with a real dataset and simulation datasets, the main results are as follows. (1) The NNA-based model encounters a relatively skewed prediction in inactive prediction and focuses more on inactive prediction, while the heuristic method has a balanced prediction. (2) The Pareto/NBD model has better repeat purchase prediction compared to that under the mean absolute error, but the NNA-based model has a better fitting in the repeat purchase distribution. (3) The distribution of estimated parameters between these two models is quite different, but is able to realize the same prediction purpose. The NNA-based model also has greater application opportunities in the commercial environment because the learned estimator is applicable to different transaction timing patterns. These findings clarify that the NNA-based model solves the estimation burden and releases the predictive power of the Pareto/NBD model.