Estimating Retail Demand with Poisson Mixtures and Out-of-Sample Likelihood

Abstract

Estimation of retail demand is critical to decisions about procuring, shipping, and shelving. The idea of Poisson demand process is central to retail inventory management and numerous studies suggest that negative binomial (NB) distribution characterize retail demand well. In this study we reassess the adequacy of estimating retail demand with the NB distribution. We propose two Poisson mixtures – the Poisson-Tweedie (PT) family and the Conway-Maxwell Poisson (CMP) distribution – as generic alternatives to the NB distribution. Based on the principle of likelihood and information theory, we adopt out-of-sample likelihood (OSL) as a metric for model selection. We test the procedure on consumer demand for 580 SKU-store sales datasets. Overall the PT family and the CMP distribution outperform the NB distribution for 70% of the tested samples. As a general case of the NB model, the PTF family has particularly strong performance for datasets with relatively small means and high dispersion. Our finding carries useful implications for researchers and practitioners who seek for flexible alternatives to the oft-used NB distribution in characterizing retail demand.