Using the Intermeans Parameter to Measure the Dispersion when Solving the Newsboy Problem

What is the best quantity of a given good that we can buy today for selling tomorrow? Obviously, the answer depends on the knowledge we have about the future trends of the market. When expressing this knowledge by a probability distribution, many assumptions are often introduced that are not founded on actual knowledge, but only on computational ease. In a former paper we have introduced the intermeans parameter as a measure of the dispersion of the demand and we have shown that the robust solution of the newsboy problem when this parameter and the mean are known is not the usual Scarf´s rule that gives the robust solution when variance and mean are known. In this paper, the statistical properties of the intermeans parameter are investigated. It will be especially discussed which properties depend on the families of distributions that are addressed and which ones are ´distribution free´. Our assertions are illustrated by numerical examples, and the information value of the various assumptions are observed