Linking Diversity and Disparity Measures

The purpose of this paper is to examine links between the diversity measures (Patil and Taillie 1982) and the disparity measures (Lindsay 1994), quantities apparently developed for somewhat different purposes. We demonstrate that numerous diversity measures satisfying all the desirable criteria mentioned by Patil and Taillie can be defined by the generating functions of certain disparities and the associated residual adjustment functions. This provides the statistician and the ecologist a wide class of flexible indices for the statistical measurement of diversity.