On some statistical properties of the apportionment index

The purpose of this paper is to initiate a statistical analysis of the Apportionment Index, a measure used in the context of forest harvesting to evaluate the fit between demand and supply distribution of logs. There have been some attempts to understand this index, but a serious theoretical foundation is still lacking. We briefly review the available literature and then proceed to investigate the properties of the index from a distributional point of view. This is mainly an exploratory article and we focus only on the cases of two and three log classes, i.e., locations. In the case of two locations we use the beta distribution for the random relative output variables; with three locations the random relative outputs are assumed to follow a singular Dirichlet distribution. Using this formulation it is possible to understand the statistical properties of the apportionment index.