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A Measure of Association for Bivariate Frailty Distributions

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  • Manatunga, Amita K.
  • Oakes, David

Abstract

A general formula is derived for the variance of Kendall's coefficient of concordance for absolutely continuous bivariate distributions generated by frailties. The formula is specialized to the case of Gumbel's Type II distribution of extreme values, which arises when the frailty has a positive stable distribution. A new diagnostic is suggested for the goodness of fit of a bivariate frailty distribution, based on the value of Kendall's tau for a truncated sample. It is shown that as a function of the proportion of the sample truncated, this truncated tau characterizes the original frailty distribution. The methods are applied to some cable insulation failure data.

Suggested Citation

  • Manatunga, Amita K. & Oakes, David, 1996. "A Measure of Association for Bivariate Frailty Distributions," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 60-74, January.
    • Handle: RePEc:eee:jmvana:v:56:y:1996:i:1:p:60-74
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    Citations

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    Cited by:

    1. Lajmi Lakhal-Chaieb & Richard J. Cook & Xihong Lin, 2010. "Inverse Probability of Censoring Weighted Estimates of Kendall's τ for Gap Time Analyses," Biometrics, The International Biometric Society, vol. 66(4), pages 1145-1152, December.
    2. Mesfioui, Mhamed & Quessy, Jean-François, 2008. "Dependence structure of conditional Archimedean copulas," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 372-385, March.
    3. Elisa Luciano & Elena Vigna, 2005. "A note on stochastic survival probabilities and their calibration," ICER Working Papers - Applied Mathematics Series 1-2005, ICER - International Centre for Economic Research.
    4. Lakhal Lajmi & Rivest Louis-Paul & Beaudoin David, 2009. "IPCW Estimator for Kendall's Tau under Bivariate Censoring," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-22, February.
    5. Alan Kimber & Shah-Jalal Sarker, 2012. "A covariance-based test for shared frailty in multivariate lifetime data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2509-2522, August.
    6. Luciano, Elisa & Spreeuw, Jaap & Vigna, Elena, 2008. "Modelling stochastic mortality for dependent lives," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 234-244, October.
    7. Derumigny Alexis & Fermanian Jean-David, 2019. "On kernel-based estimation of conditional Kendall’s tau: finite-distance bounds and asymptotic behavior," Dependence Modeling, De Gruyter, vol. 7(1), pages 292-321, January.

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