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December, 1951 Extremal Properties of Extreme Value Distributions
Sigeiti Moriguti
Ann. Math. Statist. 22(4): 523-536 (December, 1951). DOI: 10.1214/aoms/1177729542


The upper and lower bounds for the expectation, the coefficient of variation, and the variance of the largest member of a sample from a symmetric population are discussed. The upper bound for the expectation (Table 1, Fig. 1), the lower bound for the C.V. (Table 2, Fig. 4) and the lower bound for the variance (Fig. 7) are actually achieved for the corresponding particular population distributions (Figs. 2, 3, 5, 6, equation (5.1)). The rest of the bounds are not actually achieved but approached as the limits, for example, for the three-point distribution (Section 3) by letting $p$ tend to zero.


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Sigeiti Moriguti. "Extremal Properties of Extreme Value Distributions." Ann. Math. Statist. 22 (4) 523 - 536, December, 1951.


Published: December, 1951
First available in Project Euclid: 28 April 2007

zbMATH: 0044.13601
MathSciNet: MR45348
Digital Object Identifier: 10.1214/aoms/1177729542

Rights: Copyright © 1951 Institute of Mathematical Statistics

Vol.22 • No. 4 • December, 1951
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