The Annals of Mathematical Statistics

Extremal Properties of Extreme Value Distributions

Sigeiti Moriguti

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

First available in Project Euclid: 28 April 2007

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

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