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A Pragmatic Approach on Uncertainty Through Extropy as a Function of Extreme k-Records

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Abstract

The whole study has been centred on extropy treated as function of k-records to carry out analysis on uncertainty in the distribution of a random variable. The study presents some interesting properties of extropy while considering k-records instead of the parent random variable. The extropy orderings with respect to k-records arising from the random variables have been discussed in detail in this work. The study also proposes an estimator for extropy based on k-records and presents an analysis on the performance of the proposed estimator. The preference for k-records over parent random variable and classical record values has been discussed through some examples and an illustration based on a real-life data set as well.

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Data Availability

The data analysed in this study has been included from the published article of Thomas and Jose (2020)

References

  • Ayres RU, Martinàs K (1995) Waste potential entropy: the ultimate ecotoxic. Economie Appliquee 48:95–120

    Google Scholar 

  • Chandler K (1952) The distribution and frequency of record values. J Royal Stat Soci Series B (Methodol) 14:220–228

    MathSciNet  MATH  Google Scholar 

  • Contreras-Reyes JE (2015) Rényi entropy and complexity measure for skew-gaussian distributions and related families. Phys A: Stat Mech Appl 433:84–91

    Article  MathSciNet  MATH  Google Scholar 

  • Contreras-Reyes JE, Cortés DD (2016) Bounds on rényi and shannon entropies for finite mixtures of multivariate skew-normal distributions: Application to swordfish (xiphias gladius linnaeus). Entropy 18(11):382

    Article  Google Scholar 

  • David HA, Nagaraja HN (2003) Order statistics. Wiley, New York

    Book  MATH  Google Scholar 

  • Dziubdziela W, Kopociński B (1976) Limiting properties of the \(k\)th record values. Appl Math 2(15):187–190

    MATH  Google Scholar 

  • Hartley RV (1928) Transmission of information. Bell Sys Tech J 7(3):535–563

    Article  Google Scholar 

  • Jahanshahi SMA, Zarei H, Khammar AH (2020) On cumulative residual extropy. Probab Eng Inf Sci 34(4):605–625

    Article  MathSciNet  MATH  Google Scholar 

  • Jose J, Abdul Sathar E (2022) Rényi entropy on k-records and its applications in characterizing distributions. Statistics 56(3):662–680

    Article  MathSciNet  MATH  Google Scholar 

  • Jose J, Sathar EIA (2019) Residual extropy of k-record values. Stat Probab Lett 146(45):1–6

    Article  MathSciNet  MATH  Google Scholar 

  • Jose J, Sathar EIA (2021) Extropy for past life based on classical records. J Indian Soci Probab Stat 22:27–46

    Article  Google Scholar 

  • Lad F, Sanfilippo G, Agro G et al (2015) Extropy: complementary dual of entropy. Stat Sci 30(1):40–58

    Article  MathSciNet  MATH  Google Scholar 

  • Madadi M, Tata M (2014) Shannon information in k-records. Commun Stat-Theory Meth 43(15):3286–3301

    Article  MathSciNet  MATH  Google Scholar 

  • Martinas K, Frankowicz M (2000) Extropy-reformulation of the entropy principle. Periodica Polytech Chem Eng 44(1):29–38

    Google Scholar 

  • Park S (1999) A goodness-of-fit test for normality based on the sample entropy of order statistics. Stat Probab Lett 44(4):359–363

    Article  MathSciNet  MATH  Google Scholar 

  • Qiu G (2017) The extropy of order statistics and record values. Stat Probab Lett 120:52–60

    Article  MathSciNet  MATH  Google Scholar 

  • Sathar EIA, Jose J (2020) Past extropy of k-records. Stoch Quality Contr 35(1):25–38

    Article  MathSciNet  MATH  Google Scholar 

  • Sathar EIA, Jose J (2023) Extropy based on records for random variables representing residual life. Commun Stat-Simul Comp 52(1):196–206

    Article  MathSciNet  Google Scholar 

  • Shaked M, Shanthikumar JG (2007) Stochastic orders. Springer, New York

    Book  MATH  Google Scholar 

  • Shannon CE (1948) A mathematical theory of communication. Bell Sys Techn J 27(3):379–423

    Article  MathSciNet  MATH  Google Scholar 

  • Thomas PY, Jose J (2020) On weibull-burr impounded bivariate distribution. Japanese J Stat Data Sci 4(1):73–105

    Article  MathSciNet  MATH  Google Scholar 

  • Vasicek O (1976) A test for normality based on sample entropy. J Royal Stat Soci Series B (Methodol) 38(1):54–59

    MathSciNet  MATH  Google Scholar 

  • Yang J, Xia W, Hu T (2019) Bounds on extropy with variational distance constraint. Probab Eng Inf Sci 33(2):186–204

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

We would like to express our gratitude to the editors and the learned referees who have contributed to the development of this article. Their constructive comments and suggestions have been invaluable in improving the quality of this work.

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The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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    Authors and Affiliations

    1. Department of Statistics, Rajagiri College of Social Sciences, Kalamassery, Ernakulam, Kerala, 683104, India

      Jitto Jose

    2. Department of Statistics, University of Kerala, Kariavattom, Trivandrum, Kerala, 695581, India

      E. I. Abdul Sathar

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    1. Jitto Jose
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    2. E. I. Abdul Sathar
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    Contributions

    All authors contributed to the study conceptualization and design. Material preparation, conceptualization and analysis were performed by JJ. The design of the study and guidance on the overall research has been performed by EIAS. The first draft of the manuscript was written by JJ and both authors read as well as approved the final manuscript.

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    Correspondence to Jitto Jose.

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    The authors have no relevant financial or non-financial interests to disclose.

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    Jose, J., Sathar, E.I.A. A Pragmatic Approach on Uncertainty Through Extropy as a Function of Extreme k-Records. Iran J Sci 47, 837–849 (2023). https://doi.org/10.1007/s40995-023-01476-w

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    • DOI: https://doi.org/10.1007/s40995-023-01476-w

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