Tail asymptotics for the bivariate skew normal

Thomas Fung, Eugene Seneta*

*Corresponding author for this work

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    Abstract

    We derive the asymptotic rate of decay to zero of the tail dependence of the bivariate skew normal distribution under the equal-skewness condition α12, =α, say. The rate depends on whether α>0 or α<0. For the lower tail, the latter case has rate asymptotically identical with the bivariate normal (α=0), but has a different multiplicative constant. The case α>0 gives a rate dependent on α. The detailed asymptotic behaviour of the quantile function for the univariate skew normal is a key. This study is partly a sequel to our earlier one on the analogous situation for bivariate skew t.

    Original languageEnglish
    Pages (from-to)129-138
    Number of pages10
    JournalJournal of Multivariate Analysis
    Volume144
    DOIs
    Publication statusPublished - 1 Feb 2016

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    Keywords

    • Asymptotic tail dependence coefficient
    • Bivariate skew normal distribution
    • Convergence rate
    • Intermediate tail dependence
    • Quantile function
    • Residual tail dependence

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