Stochastic ordering of medians in samples from normal distributions

Abstract

In this paper, we discuss some stochastic comparisons for the sample median in a random sample from a normal distribution. Specifically, we establish that the sample median is stochastically farther than the sample mean to the population mean. To verify the result of comparison, we derive an upper bound for some distributional characteristics of the distance between the sample median and the population mean. The stochastic ordering considered here is the likelihood ratio order.

Keywords:

• Likelihood ratio order
• median
• normal distribution
• Stochastic ordering

AMS SUBJECT CLASSIFICATION:

• 60E15

Acknowledgments

The authors are very grateful to the associate editor and reviewers for their valuable comments and suggestions on earlier version of this article.