RELATIVE DIFFERENCE IN DIVERSITY BETWEEN POPULATIONS

An entropy is conceived as a functional on the space of probability di stributions. It is used as a measure of diversity (variability) of a p opulation. Cross entropy leads to a measure of dissimilarity between p opulations. In this paper, we provide a new approach to the constructi on of a measure of dissimilarity between two populations, not dependin g on the choice of an entropy function, measuring diversity. The appro ach is based on the principle of majorization which provides an intrin sic method of comparing the diversities of two populations. We obtain a general class of measures of dissimilarity and show some interesting properties of the proposed index. In particular, it is shown that the measure provides a metric on a probability space. The proposed measur e of dissimilarity is essentially a measure of relative difference in diversity between two populations. It satisfies an invariance property which is not shared by other measures of dissimilarity which are used in ecological studies. A statistical application of the new method is given.