IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v59y2018i3d10.1007_s00362-016-0804-5.html
   My bibliography  Save this article

Chernoff distance for conditionally specified models

Author

Listed:
  • Amit Ghosh

    (Rajiv Gandhi Institute of Petroleum Technology)

  • Chanchal Kundu

    (Rajiv Gandhi Institute of Petroleum Technology)

Abstract

Recently, Nair et al. (Stat Pap 52:893–909, 2011) studied Chernoff distance for truncated distributions in univariate setup. The present paper addresses the question of extending the concept of Chernoff distance to bivariate setup with focus on residual as well as past lifetimes. This measure is extended to conditionally specified models of two components having possibly different ages or failed at different time instants. We provide some bounds using likelihood ratio order and investigate several properties of conditional Chernoff distance. The effect of monotone transformation on this conditional measure has also been examined. Moreover, we study conditional Chernoff distance in context of weighted model.

Suggested Citation

  • Amit Ghosh & Chanchal Kundu, 2018. "Chernoff distance for conditionally specified models," Statistical Papers, Springer, vol. 59(3), pages 1061-1083, September.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:3:d:10.1007_s00362-016-0804-5
    DOI: 10.1007/s00362-016-0804-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-016-0804-5
    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/s00362-016-0804-5?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. Navarro, J. & Sunoj, S.M. & Linu, M.N., 2011. "Characterizations of bivariate models using dynamic Kullback-Leibler discrimination measures," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1594-1598, November.
    2. K. Nair & P. Sankaran & S. Smitha, 2011. "Chernoff distance for truncated distributions," Statistical Papers, Springer, vol. 52(4), pages 893-909, November.
    3. Johnson, N. L. & Kotz, Samuel, 1975. "A vector multivariate hazard rate," Journal of Multivariate Analysis, Elsevier, vol. 5(1), pages 53-66, March.
    4. Ebrahimi, Nader & Kirmani, S.N.U.A. & Soofi, Ehsan S., 2007. "Multivariate dynamic information," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 328-349, February.
    5. J. Navarro & S. M. Sunoj & M. N. Linu, 2014. "Characterizations of Bivariate Models Using Some Dynamic Conditional Information Divergence Measures," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(9), pages 1939-1948, May.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Nair Rohini S. & Abdul Sathar E. I., 2019. "Bivariate Dynamic Weighted Survival Entropy of Order 𝛼," Stochastics and Quality Control, De Gruyter, vol. 34(2), pages 67-85, December.
    3. Park, Sangun & Pakyari, Reza, 2015. "Cumulative residual Kullback–Leibler information with the progressively Type-II censored data," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 287-294.
    4. Colangelo Antonio, 2005. "Multivariate hazard orderings of discrete random vectors," Economics and Quantitative Methods qf05010, Department of Economics, University of Insubria.
    5. Antonio Di Crescenzo & Patrizia Di Gironimo, 2018. "Stochastic Comparisons and Dynamic Information of Random Lifetimes in a Replacement Model," Mathematics, MDPI, vol. 6(10), pages 1-13, October.
    6. M. Shafaei Noughabi & M. Kayid, 2019. "Bivariate quantile residual life: a characterization theorem and statistical properties," Statistical Papers, Springer, vol. 60(6), pages 2001-2012, December.
    7. Shaomin Wu & Hongyan Dui & Linmin Hu, 2024. "Construction of copulas for bivariate failure rates," Annals of Operations Research, Springer, vol. 341(2), pages 1177-1189, October.
    8. P. Sankaran & K. Jayakumar, 2008. "On proportional odds models," Statistical Papers, Springer, vol. 49(4), pages 779-789, October.
    9. Nazarizadeh, Farzaneh & Alemtabriz, Akbar & Zandieh, Mostafa & Raad, Abbas, 2022. "An analytical model for reliability assessment of the rail system considering dependent failures (case study of Iranian railway)," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    10. S.M. Sunoj & N. Unnikrishnan Nair, 1999. "Bivariate distributions with weighted marginals and reliablity modelling," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3-4), pages 118-126.
    11. Kundu, Debasis & Franco, Manuel & Vivo, Juana-Maria, 2014. "Multivariate distributions with proportional reversed hazard marginals," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 98-112.
    12. Belzunce, Félix & Mercader, José A. & Ruiz, José M., 2003. "Multivariate aging properties of epoch times of nonhomogeneous processes," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 335-350, February.
    13. 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.
    14. Indranil Ghosh & Osborne Banks, 2021. "A Study of Bivariate Generalized Pareto Distribution and its Dependence Structure Among Model Parameters," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 575-604, November.
    15. Navarro, J. & Sunoj, S.M. & Linu, M.N., 2011. "Characterizations of bivariate models using dynamic Kullback-Leibler discrimination measures," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1594-1598, November.
    16. Sunoj, S.M. & Sankaran, P.G., 2012. "Quantile based entropy function," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1049-1053.
    17. Hu, Taizhong & Khaledi, Baha-Eldin & Shaked, Moshe, 2003. "Multivariate hazard rate orders," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 173-189, January.
    18. Nair, N. Unnikrishnan & Sankaran, P.G., 2008. "Characterizations of multivariate life distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2096-2107, October.
    19. Gupta, Ramesh C., 2001. "Reliability Studies of Bivariate Distributions with Pareto Conditionals," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 214-225, February.
    20. N. Nair & P. Sankaran, 2014. "Modelling lifetimes with bivariate Schur-constant equilibrium distributions from renewal theory," METRON, Springer;Sapienza Università di Roma, vol. 72(3), pages 331-349, October.

    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:stpapr:v:59:y:2018:i:3:d:10.1007_s00362-016-0804-5. 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.