Sharp Expectation Bounds on Extreme Order Statistics from Possibly Dependent Random Variables

- Journal title : Communications for Statistical Applications and Methods
- Volume 11, Issue 3, 2004, pp.455-463
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CKSS.2004.11.3.455

Title & Authors

Sharp Expectation Bounds on Extreme Order Statistics from Possibly Dependent Random Variables

Yun, Seokhoon;

Yun, Seokhoon;

Abstract

In this paper, we derive sharp upper and lower expectation bounds on the extreme order statistics from possibly dependent random variables whose marginal distributions are only known. The marginal distributions of the considered random variables may not be the same and the expectation bounds are completely determined by the marginal distributions only.

Keywords

Expectation bounds;extreme order statistics;dependent random variables;

Language

English

References

1.

Arnold, B. C. (1985). $\rho$ -norm bounds on the expectation of the maximum of a possibly dependent sample. Journal of Multivariate Analysis, 17, 316-332

2.

Balakrishnan, N. (1990). Improving the Hartley-David-Gumbel bound for the mean of extreme-order statistics. Statistics and Probability Letters, 9, 291-294

3.

Gumbel, E. J. (1954). The maxima of the mean largest values and of the range. The Annals of Mathematical Statistics, 25, 76-84

4.

Hartley, H. O. and David, H. A. (1954). Universal bounds for mean range and extreme observation. The Annals of Mathematical Statistics, 25, 85-99

5.

Huang, J. S. (1998). Sequence of expectations of maximum-order statistics. Statistics and Probability Letters, 38, 117-123

6.

Lai, T. L. and Robbins, H. (1978). A class of dependent random variables and their maxima. Z. Wahrscheinlichkeitstheorie venv. Gebiete, 42, 89-111