Abstract
A two-variable generating function is described which yields the sampling probabilities of the Shannon-Wiener information measure. Expansion and collection of terms in like powers of the first variable imposes the restriction that the sum of thek category frequencies equaln; collection of terms in like powers of the second variable then produces terms whose coefficients are the required probabilities. The method may be used with either equal or unequal category probabilities for any finiten andk, and thus represents a general solution to the small sample problem. Tables of sampling probabilities are presented.
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References
Miller, G. A. and Madow, W. G. On the maximum likelihood estimate of the Shannon-Wiener measure of information. Air Force Cambridge Research Center Technical Report 54–57, 1954.
Rogers, M. S. and Green, B. F. The moments of sample information when the alternatives are equally likely. In H. Quastler (Ed.),Information theory in psychology. Glencoe, Ill.: The Free Press, 1955. Pp. 101–107.
Shannon, C. E. and Weaver, W.The mathematical theory of communication. Urbana: Univ. of Illinois Press, 1949.
Wiener, N.Cybernetics. New York: Wiley, 1948.
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The substance of this paper was reported at the meetings of the Southern Society for Philosophy and Psychology, Miami, Florida, April 12, 1963.
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Cronholm, J.N. A general method of obtaining exact sampling probabilities of the shannon-wiener measure of informationĤ . Psychometrika 28, 405–413 (1963). https://doi.org/10.1007/BF02289561
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DOI: https://doi.org/10.1007/BF02289561