The estimators of demand’s mean and standard deviation based on the observed stockout durations and the demands in the framework of the newsvendor problem with compound Poisson demand are considered. We propose also an adaptive algorithm determining the order quantity for the next period using only the result of a current one. Consider a single-product supply chain consisting of a supplier, a buyer, and customers. At the beginning of a time period T the buyer purchases a quantity Q, and replenishment during the period is impossible while the demand is random. This model is known as the newsvendor problem or single period inventory model.