Weighted extropy properties of ranked set sample for Morgenstern family of distributions

Abstract

In this paper, the weighted extropy properties of the ranked set sample are considered when the ranking is not perfect. By deriving the expression for the weighted extropy of concomitant order statistics, the expression for the weighted extropy of the ranked set sample of the study variable $ Y $ is obtained in which an auxiliary variable $ X $ is used to rank the units in each set, under the assumption that $ (X, Y) $ follows the Morgenstern family of distributions is obtained. The upper and lower bounds of the weighted extropy of the ranked set sample are obtained. The weighted extropy of the Morgenstern type bivariate uniform distribution and Morgenstern type bivariate exponential distribution are also discussed. Weighted discrimination information is also obtained between the distribution of the concomitant of the rth order statistic and the parent distribution.

Keywords

• Concomitants of order statistic
• discrimination information
• Morgenstern family of distributions
• ranked set sampling
• weighted extropy

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