## The Annals of Mathematical Statistics

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

### Extremal Properties of Extreme Value Distributions

#### 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