IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v76y2013i5p623-640.html
   My bibliography  Save this article

Generalized cumulative residual entropy and record values

Author

Listed:
  • Georgios Psarrakos
  • Jorge Navarro

Abstract

The Shannon entropy of a random variable has become a very useful tool in Probability Theory. In this paper we extend the concept of cumulative residual entropy introduced by Rao et al. (in IEEE Trans Inf Theory 50:1220–1228, 2004 ). The new concept called generalized cumulative residual entropy (GCRE) is related with the record values of a sequence of i.i.d. random variables and with the relevation transform. We also consider a dynamic GCRE obtained using the residual lifetime. For these concepts we obtain some characterization results, stochastic ordering and aging classes properties and some relationships with other entropy concepts. Copyright Springer-Verlag 2013

Suggested Citation

  • Georgios Psarrakos & Jorge Navarro, 2013. "Generalized cumulative residual entropy and record values," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(5), pages 623-640, July.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:5:p:623-640
    DOI: 10.1007/s00184-012-0408-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00184-012-0408-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00184-012-0408-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Felix Belzunce & Jorge Navarro & José M. Ruiz & Yolanda del Aguila, 2004. "Some results on residual entropy function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(2), pages 147-161, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jafar Ahmadi, 2021. "Characterization of continuous symmetric distributions using information measures of records," Statistical Papers, Springer, vol. 62(6), pages 2603-2626, December.
    2. Mao, Xuegeng & Shang, Pengjian & Wang, Jianing & Yin, Yi, 2020. "Fractional cumulative residual Kullback-Leibler information based on Tsallis entropy," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Suchandan Kayal, 2018. "On Weighted Generalized Cumulative Residual Entropy of Order n," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 487-503, June.
    4. Sun, Hongfang & Chen, Yu & Hu, Taizhong, 2022. "Statistical inference for tail-based cumulative residual entropy," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 66-95.
    5. Georgios Psarrakos, 2016. "An Operator Property of the Distribution of a Nonhomogeneous Poisson Process with Applications," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1197-1215, December.
    6. Majid Asadi & Somayeh Zarezadeh, 2020. "A unified approach to constructing correlation coefficients between random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 657-676, August.
    7. Tahmasebi Saeid & Parsa Hojat, 2019. "Notes on Cumulative Entropy as a Risk Measure," Stochastics and Quality Control, De Gruyter, vol. 34(1), pages 1-7, June.
    8. Georgios Psarrakos & Antonio Di Crescenzo, 2018. "A residual inaccuracy measure based on the relevation transform," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(1), pages 37-59, January.
    9. Tahmasebi, Saeid & Eskandarzadeh, Maryam, 2017. "Generalized cumulative entropy based on kth lower record values," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 164-172.
    10. Maryam Eskandarzadeh & Antonio Di Crescenzo & Saeid Tahmasebi, 2019. "Cumulative Measure of Inaccuracy and Mutual Information in k -th Lower Record Values," Mathematics, MDPI, vol. 7(2), pages 1-19, February.
    11. Psarrakos, Georgios & Sordo, Miguel A., 2019. "On a family of risk measures based on proportional hazards models and tail probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 232-240.
    12. Hu, Taizhong & Chen, Ouxiang, 2020. "On a family of coherent measures of variability," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 173-182.
    13. Klein, Ingo, 2017. "(Generalized) maximum cumulative direct, paired, and residual Φ entropy principle," FAU Discussion Papers in Economics 25/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    14. Antonio Di Crescenzo & Suchandan Kayal & Abdolsaeed Toomaj, 2019. "A past inaccuracy measure based on the reversed relevation transform," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(5), pages 607-631, July.
    15. Sordo, Miguel A. & Castaño-Martínez, Antonia & Pigueiras, Gema, 2016. "A family of premium principles based on mixtures of TVaRs," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 397-405.
    16. Amit Ghosh & Chanchal Kundu, 2019. "Bivariate extension of (dynamic) cumulative residual and past inaccuracy measures," Statistical Papers, Springer, vol. 60(6), pages 2225-2252, December.
    17. Xia Han & Ruodu Wang & Xun Yu Zhou, 2022. "Choquet regularization for reinforcement learning," Papers 2208.08497, arXiv.org.
    18. Abdolsaeed Toomaj & Antonio Di Crescenzo, 2020. "Connections between Weighted Generalized Cumulative Residual Entropy and Variance," Mathematics, MDPI, vol. 8(7), pages 1-27, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. K. Nair & P. Sankaran & S. Smitha, 2011. "Chernoff distance for truncated distributions," Statistical Papers, Springer, vol. 52(4), pages 893-909, November.
    2. Qin, Guyue & Shang, Pengjian, 2021. "Analysis of time series using a new entropy plane based on past entropy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Abbasnejad, M. & Arghami, N.R. & Morgenthaler, S. & Mohtashami Borzadaran, G.R., 2010. "On the dynamic survival entropy," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1962-1971, December.
    4. G. Asha & C. Rejeesh, 2015. "Characterizations using past entropy measures," METRON, Springer;Sapienza Università di Roma, vol. 73(1), pages 119-134, April.
    5. Athanasios Sachlas & Takis Papaioannou, 2014. "Residual and Past Entropy in Actuarial Science and Survival Models," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 79-99, March.
    6. Misagh, F. & Yari, G.H., 2011. "On weighted interval entropy," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 188-194, February.
    7. Kumar, Vikas, 2016. "Some results on Tsallis entropy measure and k-record values," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 667-673.
    8. Sunoj, S.M. & Sankaran, P.G., 2012. "Quantile based entropy function," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1049-1053.
    9. R. Maya & E. Abdul-Sathar & G. Rajesh & K. Muraleedharan Nair, 2014. "Estimation of the Renyi’s residual entropy of order $$\alpha $$ with dependent data," Statistical Papers, Springer, vol. 55(3), pages 585-602, August.
    10. Rajesh, G. & Abdul-Sathar, E.I. & Maya, R., 2015. "Local linear estimation of residual entropy function of conditional distributions," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 1-14.
    11. Riabi, Mehdi Yaghoobi Avval & Mohtashami Borzadaran, G.R. & Yari, G.H., 2010. "[beta]-entropy for Pareto-type distributions and related weighted distributions," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1512-1519, October.
    12. Navarro, Jorge, 2008. "Characterizations using the bivariate failure rate function," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1349-1354, September.
    13. Maya, R. & Abdul-Sathar, E.I. & Rajesh, G., 2014. "Non-parametric estimation of the generalized past entropy function with censored dependent data," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 129-135.
    14. Khorashadizadeh, M. & Rezaei Roknabadi, A.H. & Mohtashami Borzadaran, G.R., 2013. "Doubly truncated (interval) cumulative residual and past entropy," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1464-1471.
    15. Majid Asadi & Nader Ebrahimi & Ehsan S. Soofi & Somayeh Zarezadeh, 2014. "New maximum entropy methods for modeling lifetime distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(6), pages 427-434, September.
    16. Bartoszewicz, Jaroslaw, 2009. "On a representation of weighted distributions," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1690-1694, August.
    17. Asadi, Majid & Ebrahimi, Nader & Soofi, Ehsan S., 2005. "Dynamic generalized information measures," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 85-98, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metrik:v:76:y:2013:i:5:p:623-640. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.