Extropy properties of ranked set sample when ranking is not perfect

Abstract

In this article, extropy properties of the ranked set sample (RSS) when ranking is not perfect are considered. By deriving the expression for extropy of concomitant order statistic, the expression for extropy of RSS of the study variable Y in which an auxiliary variable X is used to rank the units in each set, under the assumption that $(X,Y)$ follows Morgenstern family of distributions is obtained. The upper and lower bounds of extropy of RSS are obtained. The cumulative residual extropy of concomitant of order statistic and RSS arising from Morgenstern family of distributions are also obtained. The discrimination informations between the distribution of rth RSS statistic and the parent distribution are also obtained.

Keywords:

• Ranked set sampling
• extropy
• Morgenstern family of distributions
• concomitants of order statistic
• discrimination information

Acknowledgments

The authors are thankful to the referees for their valuable comments and constructive criticism which lead to an improved version of the manuscript.