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Chernoff distance for conditionally specified models

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  • 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
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    References listed on IDEAS

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    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.
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