Open Access
December, 1949 Moments of Random Group Size Distributions
John W. Tukey
Ann. Math. Statist. 20(4): 523-539 (December, 1949). DOI: 10.1214/aoms/1177729945


A number of practical problems involve the solution of a mathematical problem of the class described in the classical language of probability theory as follows: "A number of balls are independently distributed among a number of boxes, how many boxes contain no balls, 1 ball, 2 balls, 3 balls, and so on." Problems arising in the oxidation of rubber and the genetics of bacteria are discussed as applications. A method is given of solving problems of this sort when "how many" is adequately answered by the calculation of means, variances, covariances, third moments, etc. The method is applied to a number of the simplest cases, where the number of balls is fixed, binomially distributed or Poisson and where the "sizes" of the boxes are equal or unequal.


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John W. Tukey. "Moments of Random Group Size Distributions." Ann. Math. Statist. 20 (4) 523 - 539, December, 1949.


Published: December, 1949
First available in Project Euclid: 28 April 2007

zbMATH: 0035.09304
MathSciNet: MR32966
Digital Object Identifier: 10.1214/aoms/1177729945

Rights: Copyright © 1949 Institute of Mathematical Statistics

Vol.20 • No. 4 • December, 1949
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