A weighted relative entropy method for forecasting demand

In this paper, we propose a weighted relative entropy method for forecasting demand distributions. Specifically, based on the principle of minimum relative entropy, we construct two weighted minimum relative entropy optimization models which only involve the probability vector in the empirical distribution and the estimate of the probability vector in the recent histogram. The two models may yield an updated probability distribution which is as close to the original one as possible, and furthermore, for the one without any moment constraints, we can obtain an explicit solution, whereas for the one with moment constraints, we derive its dual program that is much easier to solve than the primal problem.