Abstract: Technologies are described to provide parameter estimation for a probabilistic forecaster in inventory management. A forecaster model may be generated based on observed delivery data, demand data, and a state of a delivery system managed by an inventory management service or an enterprise resource planning service. A probability of the state of the delivery system transitioning to a subsequent state of the delivery system may be determined based on an estimation of one or more parameters using a linear regression model. In some examples, the forecaster model may be derived from the discretized version of the linear Fokker-Planck equations using maximum log-likelihood estimate with optimization through a fast marching algorithm. In other examples, Lagrange multipliers may be used to determine initial constraints on the parameters. An optimal inventory level to be maintained may be computed based on the determined probability.