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A Measure of Association for Bivariate Frailty Distributions

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  • Manatunga, Amita K.
  • Oakes, David
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 56 (1996)
    Issue (Month): 1 (January)
    Pages: 60-74

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    Handle: RePEc:eee:jmvana:v:56:y:1996:i:1:p:60-74

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    Related research

    Keywords: extreme value distribution Kendall's tau stable distributions survival analysis (null);

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    Cited by:
    1. 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.
    2. Mesfioui, Mhamed & Quessy, Jean-Fran├žois, 2008. "Dependence structure of conditional Archimedean copulas," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 372-385, March.
    3. Elisa Luciano & Jaap Spreeuw & Elena Vigna, 2006. "A note on stochastic survival probabilities and their calibration," ICER Working Papers - Applied Mathematics Series 5-2006, ICER - International Centre for Economic Research.

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