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A generalisation of Gumbel's bivariate logistic distribution

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Summary

The bivariate distributionF(x, y)=1/[1+exp(−x)+exp(−y)] was examined byGumbel. We have generalised this expression by raising it to an arbitarary power. Such a distribution may occur as a mixture of bivariate extreme-value distribution. As well as giving its basic properties, we have paid special attention to measures of correlation alternative to the product-moment, namely, Kendall's and Spearman's rank correlations and the product-moment correlation calculated after transforming the marginal distributions into Normal ones. An application to the multifactorial model of disease transmission is outlined.

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Authors and Affiliations

  1. Tranport Studies Group, Dept. of Civil and Municipal Engineering, University College London, Gower Street, WCIE 6BT, London

    S. P. Satterthwaite &  T. P. Hutchinson

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  1. S. P. Satterthwaite
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  2. T. P. Hutchinson
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Satterthwaite, S.P., Hutchinson, T.P. A generalisation of Gumbel's bivariate logistic distribution. Metrika 25, 163–170 (1978). https://doi.org/10.1007/BF02204361

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  • DOI: https://doi.org/10.1007/BF02204361

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