New Measures of Diversity
PITTSBURGH UNIV PA CENTER FOR MULTIVARIATE ANALYSIS
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The problem of measuring diversity within populations and dissimilarity or similarity between populations has been extensively treated in the literature. Diversity within populations and dissimilarity between populations have been measured and interpreted differently. The choice of a diversity measure essentially depends on the context of a problem, however any diversity measure satisfying certain basic conditions can be used for partioning the total variability into a number of additive components, each of which can be used to test a certain null hypothesis or estimate a component of the variability. Rao outlined a general procedure called Analysis of Diversity which is similar to the Analysis of Variance for quantitative data. In this direction Light and Margolin Anderson and Landis have studied the Gini-Simpson index of diversity while Nayak has extended their results for Quadratic Entaropy introduced by Rao. This paper proposes three new measures of diversity and study related inference problems. Additional keywords Concavity Convexity Computations.
- Statistics and Probability