Weighted extropies and past extropy of order statistics and k-record values

Abstract

In addition to entropy, extropy - the complementary dual of entropy has also gained importance as a measure of information in many areas. Extropy of order statistics, record values and mixed systems, residual extropy properties of k record values, past extropy have been extensively studied in literature. In this paper, we propose length (size) biased shift dependent measures of uncertainty i.e., weighted extropy and weighted residual extropy and study their monotone properties, characterization results, and some other properties in the case of order statistics and k-record values. We also discuss these studies for the past extropy measure.

Keywords:

• Extropy
• k-record values
• order statistics
• residual extropy

MATHEMATICS SUBJECT CLASSIFICATION:

• 62B10
• 94A15
• 94A17

Acknowledgments

We thank the two referees for the insightful comments and suggestions which led to an improved manuscript.

Additional information

Funding

SB would like to thank Department of Science and Technology, Government of India (Ref No. DST/INSPIRE Fellowship/2014/48) for financial assistance.