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Bivariate extension of (dynamic) cumulative residual and past inaccuracy measures

Author

Listed:
  • Amit Ghosh

    (Rajiv Gandhi Institute of Petroleum Technology)

  • Chanchal Kundu

    (Rajiv Gandhi Institute of Petroleum Technology)

Abstract

In a recent paper, Kundu et al. (Metrika 79:335–356, 2016) study the notion of cumulative residual inaccuracy (CRI) and cumulative past inaccuracy (CPI) measures in univariate setup as a generalization of cumulative residual entropy and cumulative past entropy, respectively. Here we address the question of extending the definition of CRI (CPI) to bivariate setup and study their properties. We also prolong these measures to conditionally specified models of two components having possibly different ages or failed at different time instants called conditional CRI (CCRI) and conditional CPI (CCPI), respectively. We provide some bounds on using usual stochastic order and investigate several properties of CCRI (CCPI) including the effect of linear transformation. Moreover, we characterize some bivariate distributions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:6:d:10.1007_s00362-017-0917-5
    DOI: 10.1007/s00362-017-0917-5
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    References listed on IDEAS

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    1. 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.
    2. Sangun Park & Johan Lim, 2015. "On censored cumulative residual Kullback–Leibler information and goodness-of-fit test with type II censored data," Statistical Papers, Springer, vol. 56(1), pages 247-256, February.
    3. V. Zardasht & S. Parsi & M. Mousazadeh, 2015. "On empirical cumulative residual entropy and a goodness-of-fit test for exponentiality," Statistical Papers, Springer, vol. 56(3), pages 677-688, August.
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    6. Amarjit Kundu & Chanchal Kundu, 2017. "Bivariate extension of (dynamic) cumulative past entropy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(9), pages 4163-4180, May.
    7. Debasis Kundu & Rameshwar Gupta, 2011. "Absolute continuous bivariate generalized exponential distribution," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(2), pages 169-185, June.
    8. S. Mirhosseini & M. Amini & D. Kundu & A. Dolati, 2015. "On a new absolutely continuous bivariate generalized exponential distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(1), pages 61-83, March.
    9. Antonio Di Crescenzo & Maria Longobardi, 2015. "Some properties and applications of cumulative Kullback–Leibler information," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(6), pages 875-891, November.
    10. 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.
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    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.

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