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Chernoff distance for conditionally specified models

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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.

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Acknowledgments

We are thankful to the Editor-in-Chief of the journal and anonymous reviewers for their valuable comments and suggestions leading to an improved version of the manuscript. The financial support (Ref. No. SR/FTP/MS-016/2012) rendered by the Department of Science and Technology, Government of India is acknowledged with thanks by C. Kundu for carrying out this research work.

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Authors and Affiliations

  1. Department of Mathematics, Rajiv Gandhi Institute of Petroleum Technology, Rae Bareli, 229 316, India

    Amit Ghosh & Chanchal Kundu

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  1. Amit Ghosh
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  2. Chanchal Kundu
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Correspondence to Chanchal Kundu.

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Ghosh, A., Kundu, C. Chernoff distance for conditionally specified models. Stat Papers 59, 1061–1083 (2018). https://doi.org/10.1007/s00362-016-0804-5

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