Renyi Entropy Properties of Order Statistics

Abstract

In this article, we discuss some properties of Renyi entropy and Renyi information of order statistics. Some bounds for Renyi entropy of order statistics are obtained. Also, we relate Renyi entropy ordering of order statistics to Renyi entropy ordering and other well known orderings of parent random variables. Then it is proved that the Renyi information between order statistics and parent random variable is distribution free, and it is shown, as expected, the distance is minimum for the median.

Keywords:

• Hazard function
• Ordering
• Probability integral transformation
• Renyi entropy bounds
• Renyi information

Mathematics Subject Classification:

• 62B10
• 62G30

Acknowledgments

The authors thank the referee for his/her careful reading and useful comments about this work.

The authors acknowledge the support received from Statistics Center of Excellence of Ferdowsi University of Mashhad, Iran.