THE HERMITE DISTRIBUTION AS A MODEL OF DEMAND DURING LEAD TIME FOR SLOW-MOVING ITEMS

Heretofore, the Poisson and the Laplace distributions have been used to model demand during lead time for slow-moving items. In this paper, we present a Poisson-like distribution called the Hermite. The advantage of the Hermite is that it is as simple to use as the Poisson and the Laplace are. Moreover, the Hermite is the exact distribution of demand during lead time when unit demand is Poisson, P(Λ), and lead time is normally distributed, N(μ, σ²), so long as (μ/σ²)≥Λ. Thus, the Hermite can enhance the accuracy of analysis as well as add to the tools available to the analyst.     

Theoretical considerations of the multivariate von Mises-Fisher distribution

We develop theorems that are analogous to the famous theorems of Lindley & Smith (1972) for the case that the data are from the p-variate von Mises-Fisher distribution. Results similar to those of Lindley & Smith are obtained for the two-stage case. There is, however, a departure from normal theory in the three-stage case, since closed form solutions do not exist when sampling Sfom the von Mises-Fisher distribution. The difference is discussed and elaborated.     

Empirical Bayes estimation in directional data

Empirical Bayes procedures have been developed extensively in the literature, under the assumption that the underlying parameter space (or the sample space) is Euclidean in nature. However, there has been almost no research carried out into when the data comes from a different space. We develop empirical Bayes techniques to estimate the mean direction of the Fisher-von Mises distribution. In this case, the underlying space is non-Euclidean. The special case when the data are angles on the unit circle is illustrated with an example.     

MODELING DEMAND DURING LEAD TIME*

This paper treats some of the important considerations in constructing an analytical model for the distribution of demand during lead time. It presents a formal model that can be developed along one of two lines. The first has order size and order intensity leading to a compound distribution of period demand, then period demand and lead time giving rise to a compound distribution of demand during lead time. The second has order intensity and lead time giving rise to a compound distribution of lead-time order intensity, then lead-time order intensity and order size leading to a compound distribution of demand during lead time. The paper also condenses the state of the art in a table and proposes some simple classification schemes that could help researchers extend that state of the art.