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Elementary Entropy Maximizing Probability Distributions: Analysis and Interpretation
M. J. Webber
Vol. 52, No. 3 (Jul., 1976), pp. 218-227
Published by: Clark University
Stable URL: http://www.jstor.org/stable/143269
Page Count: 10
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This paper presents complete solutions to some entropy maximizing problems. It is required to estimate the probability pi that some item falls in class i where there is associated with each class a measure xi. The distribution of probabilities is such as to maximize entropy. The paper presents methods of determining the Lagrangian multipliers which arise in the maximization process and of estimating the parameters of the resulting probability distributions. After discussing the general methods of solving such questions, three problems are considered in detail: the case in which it is known only that the sum of the probabilities over the classes equals unity; the case in which, in addition, the mean value of the variable x is known; and the case in which the sum of the probabilities and the variance of x are known. These problems are interpreted in terms of geographic results.
Economic Geography © 1976 Clark University