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December, 1948 Generalization to $N$ Dimensions of Inequalities of the Tchebycheff Type
Burton H. Camp
Ann. Math. Statist. 19(4): 568-574 (December, 1948). DOI: 10.1214/aoms/1177730152

Abstract

The Tchebycheff statistical inequality and its generalizations are further generalized so as to apply equally well to $n$-dimensional probability distributions. Comparisons may be made with other generalizations [1], [2] that have been developed recently for the two-dimensional case. The inequalities given in this paper are generally as close as the most favorable corresponding inequalities that exist for the one-dimensional case and in many simple cases they are closer than those that have been given heretofore for two dimensions. In a special case the upper bound of our inequality is actually attained. The theory contains also a less important generalization in one dimension.

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Burton H. Camp. "Generalization to $N$ Dimensions of Inequalities of the Tchebycheff Type." Ann. Math. Statist. 19 (4) 568 - 574, December, 1948. https://doi.org/10.1214/aoms/1177730152

Information

Published: December, 1948
First available in Project Euclid: 28 April 2007

zbMATH: 0037.08201
MathSciNet: MR27970
Digital Object Identifier: 10.1214/aoms/1177730152

Rights: Copyright © 1948 Institute of Mathematical Statistics

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Vol.19 • No. 4 • December, 1948
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