Abstract
Inequalities involving some sample means and order statistics are established. An upper bound of the absolute difference between the sample mean and median is also derived. Interesting inequalities among the sample mean and the median are obtained for cases when all the observations have the same sign. Some other algebraic inequalities are derived by taking expected values of the sample results and then applying them to some continuous distributions. It is also proved that the mean of a non-negative continuous random variable is at least as large as p times 100(1-p)th percentile.
| Original language | English |
|---|---|
| Pages (from-to) | 1963-1970 |
| Number of pages | 8 |
| Journal | Communications in Statistics - Theory and Methods |
| Volume | 35 |
| Issue number | 11 |
| DOIs | |
| State | Published - 1 Nov 2006 |
Bibliographical note
Funding Information:The authors gratefully acknowledge the excellent research support provided by King Fahd University of Petroleum and Minerals, Saudi Arabia. The authors also thank an anonymous referee and Prof. N. Balakrishnan for constructive suggestions that have improved the quality of the article.
Keywords
- Inequalities
- Order statistics
- Sample means
ASJC Scopus subject areas
- Statistics and Probability