Sampling Distribution of the Intermeans Parameter

Pierre L. Douillet, Besoa Rabenasolo
Laboratoire Génie et Matériaux Textiles (GEMTEX-ENSAIT)
9 rue de l'Ermitage, BP 30329,
59056 Roubaix Cedex 1, France
e-mail: {pierre.douillet, besoa.rabenasolo}@ensait.fr

Date: 28-30 August 2006

ABSTRACT:

Supply chain planning requires some knowledge of the future demand. This knowledge is often expressed by a probability distribution or, to be more robust, by some parameters that define a family of demand models, for example the family of pdfs that share a given mean and a given measure of the dispersion.

Beside the usually used standard deviation, we have introduced another measure of the dispersion: the intermeans parameter and investigated the consequences of this choice for the well known newsboy problem.

Furthermore, we have investigated the general properties of this new intermeans parameter, especially its sampling distribution, in order to obtain intervals of confidence from limited historical sales data. Closed form expressions are given for Dirac and uniform distributions. In the general case, numerical simulations have been run to obtain a better knowledge concerning this parameter.