Abstract
Shannon's measure of entropy and Gini-Simpson's diversity index are usually used by social scientists for measuring diversity of a multinomial population. In this paper entropy of order r (Renyi, A., 1961. In: Proceedings of Fourth Berkeley Symposium on Mathematics, Statistics and Probability 1, 547–561) (Renyi, 1961) is presented as a generalization of Shannon's entropy to measure and analyze the diversity. Asymptotic properties of r order index in a simple-stage cluster sampling are investigated. Also, applications to testing hypotheses are discussed. Finite sample results are computed and, to finish, a comparison of family members via moments is given.
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