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Bivariate dependence measures and bivariate competing risks models under the generalized FGM copula

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Abstract

The first part of this paper reviews the properties of bivariate dependence measures (Spearman’s rho, Kendall’s tau, Kochar and Gupta’s dependence measure, and Blest’s coefficient) under the generalized Farlie–Gumbel–Morgenstern (FGM) copula. We give a few remarks on the relationship among the bivariate dependence measures, derive Blest’s coefficient, and suggest simplifying the previously obtained expression of Kochar and Gupta’s dependence measure. The second part of this paper derives some useful measures for analyzing bivariate competing risks models under the generalized FGM copula. We obtain the expression of sub-distribution functions under the generalized FGM copula, which has not been discussed in the literature. With the Burr III margins, we show that our expression has a closed form and generalizes the reliability measure previously obtained by Domma and Giordano (Stat Pap 54(3):807–826, 2013).

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Acknowledgements

The authors thank the Editor and two anonymous reviewers for their helpful comments that improved the paper. The authors are also thankful to Prof. Christian Genest for his comments on the earlier version of the paper. This work is supported by the research grant funded by Ministry of Science and Technology, Taiwan (MOST 103-2118-M-008-MY2 and 105-2118-M-008-001-MY2).

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  1. Graduate Institute of Statistics, National Central University, No. 300, Zhongda Rd., Zhongli District, Taoyuan City, 32001, Taiwan

    Jia-Han Shih & Takeshi Emura

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  1. Jia-Han Shih
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  2. Takeshi Emura
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Correspondence to Takeshi Emura.

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Shih, JH., Emura, T. Bivariate dependence measures and bivariate competing risks models under the generalized FGM copula. Stat Papers 60, 1101–1118 (2019). https://doi.org/10.1007/s00362-016-0865-5

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