Some Results of Extropy-Based Measure of Divergence for Record Statistics

Document Type : Original Article

Authors
RITU GOEL 1
Salook U Sharma 2
Vikas Kumar 2
1 Department of Cyber Security and Digital Forensics, NFSU, Delhi.
2 Department of Applied Sciences, UIET, M. D. University, Rohtak
10.22034/jirss.2024.2026495.1057
Abstract
It is interesting to learn that the complementary dual of the Shannon entropy measure exists and has some common properties. This new measure of uncertainty has been introduced by Lad et al. (2015) and is known as extropy. Although there are some mathematical analogies between the two measures, extropy typically has different uses and interpretations than entropy. Taking into account the importance of extropy measure, and its various generalizations, in the present communication, we consider and study Kullback-Leibler based "divergence-extropy" measure between the distribution of nth upper k-record and mth upper k-record values. Characterization problems for the proposed "divergence-extropy" measure have been studied. Further, some specific lifetime distributions used in lifetime testing, physical sciences, survival analysis and reliability engineering have been studied using the proposed "divergence-extropy" measure. At the end, we study the proposed "divergence-extropy" measure between the distribution of k-record value and order statistics.
Keywords
K-L Information Measure
Extropy Measure
Divergence-Extropy Measure
Order Statistics
Record Value
Subjects
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Journal of the Iranian Statistical Society
Volume 23, Issue 1
June 2024
Pages 83-98

  • Receive Date 15 April 2024
  • Revise Date 04 September 2024
  • Accept Date 30 September 2024