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On extropy of past lifetime distribution

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Abstract

Recently Qiu [6] have introduced residual extropy as measure of uncertainty in residual lifetime distributions analogues to residual entropy (see, e.g. [3]). Also, they obtained some properties and applications of that. In this paper, we study the extropy to measure the uncertainty in a past lifetime distribution. This measure of uncertainty is called past extropy. Also it is showed a characterization result about the past extropy of largest order statistics.

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References

  1. Cover, T.M., Thomas, J.A.: Elements of Information Theory, 2nd edn. Wiley, New York (2006)

    MATH  Google Scholar 

  2. Di Crescenzo, A., Longobardi, M.: Entropy-based measure of uncertainty in past lifetime distributions. J. Appl. Probab. 39, 434–440 (2002)

    Article  MathSciNet  Google Scholar 

  3. Ebrahimi, N.: How to measure uncertainty in the residual life time distribution. Sankhya Indian J. Stat. Ser. A 58, 48–56 (1996)

    MathSciNet  MATH  Google Scholar 

  4. Krishnan, A.S., Sunoj, S.M., Nair, N.U.: Some reliability properties of extropy for residual and past lifetime random variables. J. Korean Stat. Soc. (2020). https://doi.org/10.1007/s42952-019-00023-x

    Article  MathSciNet  Google Scholar 

  5. Lad, F., Sanfilippo, G., Agrò, G.: Extropy: complementary dual of entropy. Stat. Sci. 30, 40–58 (2015)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Qiu, G., Jia, K.: The residual extropy of order statistics. Stat. Probab. Lett. 133, 15–22 (2018)

    Article  MathSciNet  Google Scholar 

  8. Shaked, M., Shanthikumar, J.G.: Stochastic Orders. Springer, Berlin (2007)

    Book  Google Scholar 

  9. Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

Francesco Buono is partially supported by the GNAMPA research group of INdAM (Istituto Nazionale di Alta Matematica) and MIUR-PRIN 2017, Project “Stochastic Models for Complex Systems” (No. 2017 JFFHSH).

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Authors and Affiliations

  1. Department of Business Management, University of Human Development, Sulaymaniyah, Iraq

    Osman Kamari

  2. Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Università degli Studi di Napoli Federico II, Naples, Italy

    Francesco Buono

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  1. Osman Kamari
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  2. Francesco Buono
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Correspondence to Francesco Buono.

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Kamari, O., Buono, F. On extropy of past lifetime distribution. Ricerche mat 70, 505–515 (2021). https://doi.org/10.1007/s11587-020-00488-7

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  • DOI: https://doi.org/10.1007/s11587-020-00488-7

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