Robust compound Poisson parameter estimation for inventory control

Most companies store demand data periodically and make periodic forecasts, whereas many processes in inventory control need parameter estimates at the individual customer level. Guidance on estimating parameters of a continuous-time process from period is lacking, particular for popular well-studied compound Poisson class demand. Whereas statistics literature typically focuses asymptotic properties, have to be estimated based limited number historical observations. We show that standard Method-of-Moments (MM) estimator – default choice applied research severely biased finite samples. The Maximum Likelihood (ML) which needs obtained by numerical search performs better, but both estimators lack robustness misspecification size distribution. propose an intuitive, consistent, closed-form MM alternative dominates ML terms estimation accuracy on-target performance. Its closed form does not depend specific distribution, making it robust easily applicable large-scale applications with items. In case study, we find loss due storing four times as high under proposed estimator.