IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v81y2018i1d10.1007_s00184-017-0633-0.html
   My bibliography  Save this article

A residual inaccuracy measure based on the relevation transform

Author

Listed:
  • Georgios Psarrakos

    (University of Piraeus)

  • Antonio Di Crescenzo

    (Università di Salerno)

Abstract

Inaccuracy and information measures based on the cumulative residual entropy are useful in various fields, and are attracting increasing attention in Probability Theory and Statistics. In this paper, we introduce and study an inaccuracy measure concerning the relevation transform of two nonnegative continuous random variables. We investigate various distributional properties and characterization results that are based on the mean residual lifetime and involve the generalized Pareto distribution. A connection with the proportional hazards model is also provided. We obtain comparison results involving the proposed inaccuracy measure and some existing inaccuracy measures. Some illustrative examples are finally given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:81:y:2018:i:1:d:10.1007_s00184-017-0633-0
    DOI: 10.1007/s00184-017-0633-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-017-0633-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-017-0633-0?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. Vikas Kumar & H. Taneja & R. Srivastava, 2011. "A dynamic measure of inaccuracy between two past lifetime distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(1), pages 1-10, July.
    2. 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.
    3. Erhard Cramer & Udo Kamps, 2003. "Marginal distributions of sequential and generalized order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(3), pages 293-310, December.
    4. M. Burkschat & J. Navarro, 2014. "Asymptotic behavior of the hazard rate in systems based on sequential order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(8), pages 965-994, November.
    5. J. Navarro & Y. Aguila & J. Ruiz, 2001. "Characterizations through reliability measures from weighted distributions," Statistical Papers, Springer, vol. 42(3), pages 395-402, July.
    6. Balakrishnan, N. & Kamps, U. & Kateri, M., 2009. "Minimal repair under a step-stress test," Statistics & Probability Letters, Elsevier, vol. 79(13), pages 1548-1558, July.
    7. Nuria Torrado & Rosa E. Lillo & Michael P. Wiper, 2012. "Sequential Order Statistics: Ageing and Stochastic Orderings," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 579-596, September.
    8. 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.
    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. P. G. Sankaran & M. Dileep Kumar, 2019. "Reliability properties of proportional hazards relevation transform," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 441-456, May.
    3. 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.
    4. 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.

    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. M. Burkschat & J. Navarro, 2014. "Asymptotic behavior of the hazard rate in systems based on sequential order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(8), pages 965-994, November.
    2. Tanmay Sahoo & Nil Kamal Hazra & Narayanaswamy Balakrishnan, 2024. "Multivariate stochastic comparisons of sequential order statistics with non-identical components," Statistical Papers, Springer, vol. 65(7), pages 4365-4404, September.
    3. Psarrakos, Georgios & Toomaj, Abdolsaeed & Vliora, Polyxeni, 2024. "A family of variability measures based on the cumulative residual entropy and distortion functions," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 212-222.
    4. 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.
    5. Maryam Esna-Ashari & Narayanaswamy Balakrishnan & Mahdi Alimohammadi, 2023. "HR and RHR orderings of generalized order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 131-148, January.
    6. 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.
    7. Burkschat, Marco & Torrado, Nuria, 2014. "On the reversed hazard rate of sequential order statistics," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 106-113.
    8. Félix Belzunce & Carolina Martínez-Riquelme & José A. Mercader & José M. Ruiz, 2021. "Comparisons of policies based on relevation and replacement by a new one unit in reliability," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 211-227, March.
    9. Jafar Ahmadi, 2021. "Characterization of continuous symmetric distributions using information measures of records," Statistical Papers, Springer, vol. 62(6), pages 2603-2626, December.
    10. Erhard Cramer & Jorge Navarro, 2015. "Progressive Type‐II censoring and coherent systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(6), pages 512-530, September.
    11. Marco Burkschat & Tomasz Rychlik, 2018. "Sharp inequalities for quantiles of system lifetime distributions from failure-dependent proportional hazard model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 618-638, September.
    12. P. Sankaran & S. Sunoj, 2004. "Identification of models using failure rate and mean residual life of doubly truncated random variables," Statistical Papers, Springer, vol. 45(1), pages 97-109, January.
    13. 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.
    14. Tahmasebi, Saeid & Eskandarzadeh, Maryam, 2017. "Generalized cumulative entropy based on kth lower record values," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 164-172.
    15. 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.
    16. van Bentum, Thomas & Cramer, Erhard, 2019. "Stochastic monotonicity of MLEs of the mean for exponentially distributed lifetimes under hybrid censoring," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 1-8.
    17. Maryam Esna-Ashari & Mahdi Alimohammadi & Elnaz Garousi & Antonio Di Crescenzo, 2024. "Some New Results on Stochastic Comparisons of Spacings of Generalized Order Statistics from One and Two Samples," Mathematics, MDPI, vol. 12(10), pages 1-19, May.
    18. Navarro, Jorge & Arriaza, Antonio & Suárez-Llorens, Alfonso, 2019. "Minimal repair of failed components in coherent systems," European Journal of Operational Research, Elsevier, vol. 279(3), pages 951-964.
    19. Amini, Morteza & Balakrishnan, N., 2013. "Nonparametric meta-analysis of independent samples of records," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 70-81.
    20. Bedbur, Stefan & Johnen, Marcus & Kamps, Udo, 2019. "Inference from multiple samples of Weibull sequential order statistics," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 381-399.

    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:81:y:2018:i:1:d:10.1007_s00184-017-0633-0. 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.