The Annals of Mathematical Statistics

Extremal Properties of Extreme Value Distributions

Sigeiti Moriguti

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Abstract

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.

Article information

Source
Ann. Math. Statist., Volume 22, Number 4 (1951), 523-536.

Dates
First available in Project Euclid: 28 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177729542

Digital Object Identifier
doi:10.1214/aoms/1177729542

Mathematical Reviews number (MathSciNet)
MR45348

Zentralblatt MATH identifier
0044.13601

JSTOR
links.jstor.org

Citation

Moriguti, Sigeiti. Extremal Properties of Extreme Value Distributions. Ann. Math. Statist. 22 (1951), no. 4, 523--536. doi:10.1214/aoms/1177729542. https://projecteuclid.org/euclid.aoms/1177729542


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